All-optical modulation and sdwitching with patterned optically absorbing polymers

ABSTRACT

All-optical processing devices that include patterned optically active polymers. The devices that are constructed according to principles of the invention include at least one optical input port and at least one optical output port, respectively configured to accept optical input signals and provide optical output signals. The devices include optically active material such as organic polymers that interact with illumination at a first wavelength to change at least one optical property in a non-linear manner. The optically active polymer can be placed adjacent one or more waveguides that allow the input illumination to propagate. As the optical property of the optically active material is changed by the incident illumination, the propagating illumination undergoes a modulation or change in phase, thereby providing an optical output signal having a desired relation to the optical input signal, such as the result of a logical or a computational operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and the benefit of co-pending U.S.provisional patent application Ser. No. 61/056,544, filed May 28, 2009which application is incorporated herein by reference in its entirety,and this application is a continuation-in-part of co-pendingInternational Application PCT/U.S.09/36128, filed Mar. 5, 2009, whichdesignated the United States, and which itself claimed priority to andthe benefit of then co-pending U.S. provisional patent application Ser.No. 61/068,326, filed Mar. 5, 2008, each of which applications isincorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The invention relates to systems and methods for optical modulationusing optical waveguides in general and particularly to systems andmethods for optical modulation using optical waveguides, including splitwaveguides, which employ materials, such as polymers, having largenonlinear optical characteristics.

BACKGROUND OF THE INVENTION

The field of nonlinear optics is extremely rich in results, and has beenaround for many years. Basically the premise of nearly all measurementsin the field is that one introduces a sufficiently high power flux (or“fluence,” a term of art) in an optical material, it is often possibleto excite nonlinear behavior, meaning that the properties of thematerial change with the input optical power. This kind of effect isvery often described through the use of, for instance. Chi² (χ²) andChi³ (χ³) which are material dependent constants that describe thestrength of two of the relevant nonlinear optical activities of amaterial. Some nonlinearities, which are material dependent, will workat the full optical frequency, while others are slower. Recently,engineered organic materials have begun to be used for nonlinear optics,because they can be designed to have extremely large χ² and χ³ moments.

There is a need for systems and methods that can fully exploit theoptical properties of materials that exhibit nonlinear behavior withouthaving to provide excessive amounts of optical power to do so.

SUMMARY OF THE INVENTION

In one aspect, the invention relates to an all-optical signal processingdevice. The all-optical processing device comprises an optical input ofthe all-optical signal processing device configured to receive anoptical signal as input; an optical output of the all-optical signalprocessing device configured to provide a modulated optical signal asoutput; and a plurality of interaction regions configured to permit theoptical input signal to interact in each of the plurality of interactionregions with a selected cladding comprising a material that exhibits anodd order nonlinear optical coefficient to produce an optical outputsignal, the interaction region comprising a high index contrastwaveguide adjacent an insulating surface of a substrate.

In one embodiment, each of the plurality of interaction regions isconfigured to permit the optical input signal to interact with at leastanother optical signal. In one embodiment, the high index contrastwaveguide is a selected one of a ridge waveguide, a rib and a slotwaveguide. In one embodiment, the high index contrast slot waveguide hasat least two stripes defining the slot; and at least some of thecladding is situated within the slot. In one embodiment, the slot isless than or equal to 100 nanometers in width.

In one embodiment, the substrate is a silicon wafer. In one embodiment,the insulating surface is a layer comprising silicon and oxygen. In oneembodiment, the substrate is selected from one of silicon-on-insulator(SOI) and silicon-on-sapphire (SOS).

In one embodiment, the optical input comprises an input waveguide forcoupling optical radiation into the high index contrast waveguide.

In one embodiment, the all-optical signal processing device is a logicgate. In one embodiment, the logic gate is a selected one of an ANDgate, an OR gate, a NAND a NOR, and an XOR gate. In one embodiment, theall-optical signal processing device is a selected one of an opticallatch and an optical memory. In one embodiment, the all-optical signalprocessing device is a variable delay line. In one embodiment, theall-optical signal processing device is a self-oscillator. In oneembodiment, the all-optical signal processing device is a multiplexer.In one embodiment, the all-optical signal processing device is ademultiplexer. In one embodiment, the all-optical signal processingdevice is a selected one of a clock and a clock multiplier. In oneembodiment, the cladding material is infiltrated into a slot of a slotwaveguide. In one embodiment, the cladding material, upon absorbingsingle or multiple photons of one frequency, produces a local change inrefractive index or dielectric constant for propagating modes of anotherfrequency. In one embodiment, a system comprises a plurality of suchdevices on the same substrate, each of which may comprise differentcladding materials.

The foregoing and other objects, aspects, features, and advantages ofthe invention will become more apparent from the following descriptionand from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the invention can be better understood withreference to the drawings described below, and the claims. The drawingsare not necessarily to scale, emphasis instead generally being placedupon illustrating the principles of the invention. In the drawings, likenumerals are used to indicate like parts throughout the various views.

FIG. 1 is a diagram showing dispersion plots for the fundamental mode(Ex polarized) of exemplary clad and unclad waveguides, shown aseffective index vs. wavelength in μm.

FIG. 2 is a diagram showing an SEM image of an exemplary ring resonator.

FIG. 3 is a diagram showing the normalized transmission of light throughthe system (and past the ring) in dB, as a function of wavelengthdetuning in nm for both clad and unclad waveguides, shifted to overlayresonance peaks.

FIG. 4 is a diagram showing an exemplary slot waveguide mode profile.

FIG. 5 is a diagram showing the effective index vs. free spacewavelength in microns for the slot waveguide of FIG. 4.

FIG. 6 is a diagram showing the device layout of an exemplary slotwaveguide.

FIG. 7 is a diagram showing an SEM image of a portion of an oval slotwaveguide.

FIG. 8 is a diagram showing a more detailed SEM image showing thecoupling region of an exemplary slot waveguide and an input waveguide.

FIG. 9 is a diagram showing the measured transmission spectrum in dB vs.laser wavelength in nm past a high quality factor slot ring resonator.

FIG. 10 is a diagram showing the detail of the peak of the transmissionspectrum near 1488 nm.

FIG. 11 is a diagram showing a shallow angle SEM view of a typicalsilicon-on-insulator ring resonator and waveguide having a sidewallroughness on the order of 10 nm.

FIG. 12 is a diagram of a slot ring resonator directional couplerregion, and the associated input waveguide.

FIG. 13 is a diagram showing a slot waveguide structure that exhibitssubfield stitching errors at the edge of an input waveguide.

FIG. 14 is a diagram showing yet another example of a rough wall that islikely to create problems in device fabrication and operation.

FIG. 15 is a diagram showing an exemplary high-index segmented waveguidestructures, which in the embodiment shown comprises a central waveguideportion with fingers or ridges sticking out to the sides.

FIG. 16A is a diagram that shows a dispersion diagram of both asegmented waveguide and the normal, unsegmented waveguide, taken on aplane parallel to the substrate that on a z plane that intersects themiddle of a segment.

FIG. 16B is a diagram that shows modal patterns of the Bloch mode, withcontours of |E| plotted, starting at 10% of the max value and withcontour increments of 10%.

FIG. 16C is a diagram that shows a plot of modal patterns over fourperiods of a segmented waveguide on a horizontal plane that intersectsthe silicon layer halfway through.

FIG. 17 is a diagram that shows an exemplary electrical isolator thatwas constructed and tested, and which provided both a transition from astandard to a slotted waveguide and electrical isolation between the twosides of the slot waveguide.

FIG. 18 is a diagram showing the results of a baseline measurement of anEDFA and optical test system in the absence of a test sample.

FIG. 19 is a diagram showing the results for the measurement of a firstexemplary material having a large value of χ³.

FIG. 20 is a diagram showing the results for the measurement of a secondexemplary material having a large value of χ³.

FIG. 21 is a diagram that shows a plot of the numerically computedconversion efficiency for the second exemplary material having a largevalue of χ³, in dB vs 1 watt compared to length traveled in waveguide inμm.

FIG. 22 is a diagram showing a chemical reaction useful for thesynthesis of a chromophore referred to as YLD 124.

FIG. 23 is a four panel diagram that shows details of one embodiment ofan optical modulator device, including the geometry of thephotodetectors and filters, and including a cross section of the slottedwaveguide.

Panel A of FIG. 24 shows the transmission spectrum of detector device 1,according to principles of the invention.

Panel B of FIG. 24 shows the transmission spectrum of detector device 2,according to principles of the invention.

Panel C of FIG. 24 shows several curves of current vs. power for threemeasurement series.

Panel D of FIG. 24 shows the output current as a function of wavelength,overlaid with the transmission spectrum.

FIG. 25 is a diagram showing the use of the structures embodying theinvention as resonantly enhanced electro-optic modulators, and a resultat approximately 6 MHz operating frequency.

FIG. 26 is a diagram showing a chemical formula for the chromophorereferred to as JSC1.

FIG. 27 shows a diagram of a Mach-Zehnder modulator with a conventionalelectrode geometry in top-down view, including top contact, waveguide,and bottom contact layers.

FIG. 28 is an isometric three dimensional schematic of a conventionalMach-Zehnder polymer interferometer, showing top contact, waveguide, andbottom contact layers.

FIG. 29 is a three dimensional, isometric schematic of a slot-waveguidemodulator, showing the slot waveguide, segmentation region and metalcontacts. The device illustrated in FIG. 29 functions by maintaining thetwo arms of the slot waveguide at differing voltages, creating a strongelectric field in the slot.

FIG. 30 is a top-down view of a layout of a slot-waveguide based opticalmodulator of the device in FIG. 29.

FIG. 31A shows the optical mode with |E| plotted in increments of 10%,for a mode with propagating power of 1 Watt.

FIG. 31B shows a contour plot of the static electric field for thewaveguide of FIG. 31A with the field of view slightly enlarged.

FIG. 31C and FIG. 31D show analogous data to FIG. 31A and FIG. 31B,respectively, for the most optimal slot waveguide geometry that ispresently known to the inventors (corresponding to design #3 in Table2).

FIG. 32A shows the static voltage potential field distribution due tocharging the two electrodes.

FIG. 32B shows the electric field due to the potential distribution. |E|is plotted in increments of 10%.

FIG. 33 is a diagram that illustrates the dependence of susceptibilityon gap size for several waveguide designs.

FIG. 34A shows a cross section of the segmented, slotted waveguide, withthe |B| field plotted in increments of 10% of max value.

FIG. 34B shows a similar plot for the unsegmented waveguide.

FIG. 34C shows a horizontal cross section of the segmented, slottedwaveguide in which Re(Ex) is plotted in increments of 20% of max.

FIG. 35( a) is a diagram of the silicon slot waveguide used in theMach-Zehnder modulator, according to principles of the invention.

FIG. 35( b) is an SEM micrograph of a slot waveguide, according toprinciples of the invention.

FIG. 36( a) is a diagram of the modulator layout, according toprinciples of the invention.

FIG. 36( b) and FIG. 36( c) are two SEM micrographs of modulatorsconstructed according to principles of the invention, that show theslotted, segmented region, as well as the location where the siliconmakes contact with the electrical layer.

FIG. 37 is an SEM micrograph a silicon ridge waveguide about 0.5 μm widethat is used in a y-junction coupler.

FIG. 38 is a schematic diagram showing an illustrative design of anall-optical switch.

FIG. 39 is a schematic diagram showing an illustrative design of multistage logic gate with two types of absorbing materials.

FIG. 40 is a schematic diagram showing an illustrative design of an alloptical switch comprising a ring resonator.

FIG. 41 is a schematic diagram showing an alternative design forresonant enhancement using an absorption based index shift.

DETAILED DESCRIPTION OF THE INVENTION

High index contrast waveguides as described herein are useful toconcentrate light in order to enhance nonlinear optical effects invarious materials so that such effects can be employed to manipulatelight (or more generally electromagnetic radiation) at low power levels,as compared to conventional systems and methods that employ nonlinearoptical materials. The manipulation of electromagnetic radiation orlight can be useful to provide a variety of components that performoperations on light such as rectification and logic operations in amanner analogous to the same operations which are provided usingelectronic devices operating on electrical signals. For example, aninput a light wave to be processed is impressed onto the component. Thelight wave has at least one parameter characterizing the light wave,such as one of an intensity, a polarization, a frequency, a wavelength,and a duration (e.g., a pulse length, or in the case of continuous wavelight, an effectively infinite duration). After the input light wave isprocessed (or interacts with the waveguide and the clad nonlinearoptical material adjacent to the waveguide), an output signal isobserved. In a circumstance where the input signal has been processed,the output signal has at least one parameter that is different from atleast one parameter characterizing the input light wave, includingpossibly an electrical output signal when the input light wave had noelectrical signal component (e.g., optical rectification). As usedherein, the term “optical rectification” is intended to relate to inputsignals having frequencies ranging from of the order of 100s ofgigahertz through terahertz, and also including IR, visible, UV_(π) andx-ray input signals.

As described in greater detail herein, the present invention providesmethods and structures that exhibit enhancement of the nonlinear effectsin various electro-optical materials that is sufficient to make thenonlinear effects accessible with continuous-wave, low-power lasers. Insome embodiments, pulsed lasers can be used in addition to or in placeof CW lasers. As is described herein the waveguide is coated or cladwith another material which provides or exhibits an enhanced nonlinearoptical coefficient, such as certain kinds of organic electro-opticalmaterials that can be specifically designed to operate in variousregions of the electromagnetic spectrum. We have demonstrated that somedesigns of high index contrast waveguides are designed to concentratelight in the cladding. In some embodiments, the waveguide is a splitwaveguide. In some embodiments, the split waveguide is coated with amaterial which provides an enhanced nonlinear optical coefficient. Insome embodiments, the waveguides of the invention, including slotted orsplit waveguides, can operate with a low optical index fluid as acladding, for example, air, or with no cladding, for example, vacuum. Insome embodiments, the coating or cladding can be a ferroelectricmaterial. In some embodiments, the two sides of the split waveguide alsocomprise electrodes that are used for polling a χ² material introducedinto the gap. As described herein, in some embodiments, the dispersionof a waveguide is engineered to enhance the optical power in the mode byslowing the propagation of the light. In some embodiments the waveguidesare segmented waveguides. As discussed herein, the waveguide can provideoptical field enhancement when the structure is arranged into aresonator, which in various embodiments can be either a ring resonatoror a linear resonator. It is believes that appropriate claddings cancomprise one or more of glass, semiconductor, quantum dots, saturableabsorbers, quantum dots doped into an organic mains, electro-opticmaterials such as polymers and dendrimers, polymers or other organicmaterials providing large χ³ coefficients, or other nonlinear opticalmaterial to provide large optical nonlinearities through fieldenhancement in the cladding. In some embodiments, the systems andmethods of the invention can be used to provide a tunable infraredsource. In some embodiments, by using a low power tunable laser and ahigh power fixed wavelength laser as the inputs, it is possible toproduce a high power coherent tunable source. The tunable source can bea widely tunable coherent source. In addition, using systems and methodsof the invention, the use of an incoherent input light source can resultin an incoherent tunable source. With the provision of on-chip feedback,the systems and methods of the invention can be used to provide devicesthat exhibit optical self-oscillation. In some embodiments, the centralhigh index waveguide comprises an amplifying medium, such as a galliumarsenide stripe laser. In some embodiments, where the cladding materialexhibits nonlinearities, the laser can be operated as a pulsed source.In some embodiments, systems and methods of the invention can beconstructed to provide optical logic functionality, such as optical ANDor optical flip-flops. It is believed that systems and method accordingto the invention can be employed to create optical NAND, OR, NOR and XORgates, and optical latches, or optical memory. In some embodiments, thesystems of the invention can further comprise pump lasers integratedonto the same chip. In some embodiments, the systems of the inventioncan further comprise off-chip feedback or amplification for frequencyconversion or pulse generation. In some embodiments, an additionalelectrical signal is coupled into the structure to provide activemodelocking.

We have developed a set of tools for concentrating light to a highdegree by using silicon or other high index contrast waveguides, and wehave fabricated devices that demonstrate some of the many applicationsthat can be contemplated when such nonlinear materials are exploited.While the description given will be expressed using single crystalsilicon, it is believed that similar devices, systems and methods can beprovided using polycrystalline silicon (“poly silicon”) or amorphoussilicon (also referred to as “a-silicon” or “α-silicon”). In particular,by utilizing split waveguides (or slot waveguides), we are able togreatly enhance the optical fields in the cladding of a tightly confinedwaveguide, without greatly enhancing the optical losses of the samewaveguide. Combining the high field concentrations available from thesplit waveguides with the high nonlinear activity of nonlinear opticalpolymers permits the development of nonlinear optical devices operatingat much lower optical input power levels than are possible withconventional free space or chip based systems. We have demonstratedfour-wave mixing (which is based upon χ³), as well as opticalrectification (based on χ²), in such waveguides. Using these waveguidesit is possible to decrease the power levels needed to observesignificant nonlinearities to the point where, by contrast withconventional nonlinear optics, it can be done with non-pulsed,continuous wave lasers.

Chi2 (χ²) and Chi3 (χ³) based optical effects can be used in particularto build on-chip optical parametric oscillator (“OPO”) systems, wheretwo input wavelengths can be mixed together to produce sum anddifference frequencies. These frequencies can be either higher or lowerthan the input frequencies, and can be made tunable. These effects workfor frequencies from the ultraviolet and X-ray regime all the way outinto the far infrared and microwave, and in fact can work down to DC insome cases, particularly with optical rectification.

The material of which the high index waveguide is made can be anymaterial having a high index that is reasonably transparent at thewavelengths of interest. This can include but is not limited to silicon,gallium nitride, indium phosphide, indium gallium nitride, galliumphosphide, diamond, sapphire, or the various quaternary III/V and II/VImaterials such as aluminum gallium arsenide phosphide. III/V denotesmaterials having at least one element from column III of the periodictable of elements (or an element that is stable as a positive trivalention) and at least one element from column V (or an element that isstable as a negative trivalent ion). Examples of III/V compounds includeBN, AlP, GaAs and InP. II/VI denotes materials having at least oneelement from column II of the periodic table of elements (or an elementthat is stable as a positive divalent ion) and at least one element fromcolumn VI (or an element that is stable as a negative divalent ion).Examples of II/VI compounds include MgO, CdS, ZnSe and HgTe.

We will now present a more detailed description of the systems andmethods of the invention, including successively the mechanicalstructure of exemplary embodiments of high index waveguides, exemplaryembodiments of cladding materials having large nonlinear constants χ²and χ³ and their incorporation into devices having high indexwaveguides, exemplary results observed on some of the fabricated devicesthat are described, and some theoretical discussions about the devicesand the underlying physics, as that theory is presently understood.Although the theoretical descriptions given herein are believed to becorrect, the operation of the devices described and claimed herein doesnot depend upon the accuracy or validity of the theoretical description.That is, later theoretical developments that may explain the observedresults on a basis different from the theory presented herein will notdetract from the inventions described herein.

Exemplary High Index Waveguide Structures Example 1 High-Q RingResonators in Thin Silicon-on-Insulator

Resonators comprising high-Q microrings were fabricated from thinsilicon-on-insulator (SOI) layers. Measured Q values of 45 000 wereobserved in these rings, which were then improved to 57 000 by adding aPMMA cladding. Various waveguide designs were calculated, and thewaveguide losses were analyzed. It is recognized that several forms ofsilicon on insulator, such as SOI comprising wafers having a siliconoxide layer fabricated on silicon, or such as silicon on sapphire (SOS)can be used in different embodiments.

Microring resonator structures as laser sources and as optical filterelements for dense wavelength division multiplexing systems have beenstudied in the past. The silicon-on-insulator (SOI) structure describedhere is particularly advantageous. It has low waveguide loss. One canextrapolate an uncoupled Q value of 94 000 and a waveguide loss of 7.1dB/cm in the unclad case, and −6.6 dB/cm in the PMMA clad case, from therespective measured Q values of 45 000 and 57 000. Although higher Qvalues have been obtained for optical microcavities, we believe that ourgeometry has the highest Q for a resonator based on a single modesilicon waveguide. It is also noteworthy that a large amount of powerappears outside the core silicon waveguide, which may be important insome applications. The modes that are described herein haveapproximately 57% of the power outside the waveguide, as compared to 20%for a single-mode 200-nm-thick silicon waveguide, and 10% for asingle-mode 300-nm-thick silicon waveguide.

In the embodiment now under discussion, wafer geometries were selectedthat minimize the thickness of the SOI waveguiding layer as well as theburied oxide, but still yield low loss waveguides and bends. A number ofdifferent waveguide widths were compared by finite difference based modesolving. The geometry used in the exemplary embodiment comprises a500-nm-wide waveguide formed in a 120-nm-thick silicon layer, atop a 1.4μm oxide layer, which rests on a silicon handle, such as a silicon waferas a substrate. Such a configuration supports only a singlewell-contained optical mode for near infrared wavelengths. Thedispersion characteristics are shown in FIG. 1 for both unclad andPMMA-clad waveguides. Our interest in unclad structures stems from theease of fabrication, as detailed in the following, as well as theflexibility an open air waveguide may provide for certain applications.

These modes were determined by using a finite difference based Hermitianeigensolver, described further herein. It is possible to calculate theloss directly from the mode pattern with an analytic method valid in thelow-loss limit. The waveguide loss at 1.55 μm calculated in such afashion is approximately −4.5 dB. This loss figure was in agreement withthe extrapolated results of FDTD simulation.

Because a loss of −4 dB/cm is attributed to substrate leakage, thewaveguide loss can be improved by the addition of a cladding, whichtends to pull the mode upwards. This notion is supported by the measureddecrease in waveguide loss upon the addition of a PMMA cladding. It canbe shown that the substrate leakage loss attenuation coefficient isnearly proportional to

e ^(−2√){square root over (^(n) ^(eff) ² ^(-n) ⁰ ² )}^(k) ⁰ ^(A)

if k₀ is the free space wave number, n_(eff) is the effective index ofthe mode, n₀ is the effective index of the oxide layer, and A is thethickness of the oxide. In the present case, the e-folding depth of theabove-mentioned function turns out to be 180 nm, which explains why thesubstrate leakage is so high.

SOI material with a top silicon layer of approximately 120 nm and 1.4 μmbottom oxide was obtained in the form of 200 mm wafers, which weremanually cleaved, and dehydrated for 5 min at 180° C. The wafers werethen cleaned with a spin/rinse process in acetone and isopropanol, andair dried. HSQ electron beam resist from Dow Corning Corporation wasspin coated at 1000 rpm and baked for 4 min at 180° C. The coatedsamples were exposed with a Leica EBPG-5000+electron beam writer at 100kV. The devices were exposed at a dose of 4000 μc/cm², and the sampleswere developed in MIF-300 TMAH developer and rinsed with water andisopropanol. The patterned SOI devices were subsequently etched by usingan Oxford Plasmalab 100 ICP-RIE within 12 mTorr of chlorine, with 800 Wof ICP power and 50 W of forward power applied for 33 s. Microfabricateddevices such as the one shown in FIG. 2 were tested by mounting the diesonto an optical stage system with a single-mode optical fiber array. Atunable laser was used first to align each device, and then swept inorder to determine the frequency domain behavior of each of the devices.Light was coupled into the waveguides from a fiber mode by the use ofgrating couplers. Subsequently the devices were spin-coated with 11% 950K PMMA in Anisole, at 2000 rpm, baked for 20 min at 180° C., andretested.

The theoretical development of the expected behavior of a ring resonatorsystem has been described in the technical literature. In the presentcase the dispersion of the waveguide compels the addition of adispersive term to the peak width. We take λ₀ to be the free spacewavelength of a resonance frequency of the system, n₀ to be the index ofrefraction at this wavelength, (δn/δλ)₀, the derivative of n withrespect to λ taken at λ₀, L to be the optical path length around thering, a to be the optical amplitude attenuation factor due to loss in asingle trip around the ring, and finally t to be the optical amplitudeattenuation factor due to traveling past the coupling region. In thelimit of a high Q, and thus

(1−α)

1 and (1−t)

1,

we have

$\begin{matrix}{Q = {\frac{\pi \; L}{\lambda_{0}}{\frac{( {n_{0} - {\lambda_{0}( \frac{\partial n}{\partial\lambda} )}_{0}} )}{( {1 - {\alpha \; t}} )}.}}} & (1)\end{matrix}$

The waveguide mode was coupled into a ring resonator from an adjacentwaveguide. As shown in FIG. 2, the adjacent waveguide can in someembodiments be a linear waveguide. The strength of coupling can then belithographically controlled by adjusting the distance between thewaveguide and the ring. This ring was fabricated with a radius of 30 μm,a waveguide width of 500 nm, and a separation between ring and waveguideof 330 nm. For the clad ring presented, the measured Q is 45 000, andthe extinction ratio is −22 dB, for the resonance peak at 1512.56 nm.The PMMA clad ring had a similar geometry, and achieved a Q of 57 000,but with an extinction ratio of −15.5 dB. Typical observed transmissionspectra are shown in FIG. 3. The typical amount of optical power in thewaveguide directly coupling into the resonator was about 0.03 mW. Adependence of the spectrum on this power was not observed, to within anorder of magnitude.

From the mode-solving results for the unclad waveguides, we have(δn/δλ)(1.512)=−1.182 μm⁻¹, and n(λ=1.512)=1.688. Using this result andthe earlier relations, the waveguide loss can be calculated from themeasured Q value. Specifically, an extinction that is at least −22 dBindicates that a critically coupled Q in this geometry is greater than38 500, which then implies a waveguide loss of less than −7.1 dB/cm. Insimilar fashion, the PMMA clad waveguide resonator with a Q of 57 000but only −15.5 dB of extinction allows a worst case waveguide loss of−6.6 dB/cm. This also implies an intrinsic Q of 77 000 for the uncladresonator, and an intrinsic Q of 94 000 for the PMMA clad resonator.

These devices have a slight temperature dependence. Specifically, theresonance peak shifts correspondingly with the change in the refractiveindex of silicon with temperature, moving over 2 nm as temperatureshifts from 18 to 65° C. The Q rises with higher temperatures slightly,from 33 k at 18° C. to 37 k on one device studied. This shift canprobably be explained entirely by the dependence of Q on the effectiveindex.

Example 2 High-Q Optical Resonators in Silicon-on-Insulator Based SlotWaveguides

We now describe the design, fabrication and characterization of high Qoval resonators based on slot waveguide geometries in thin silicon oninsulator material. Optical quality factors of up to 27,000 weremeasured in such filters, and we estimate losses of −10 dB/cm in theslotted waveguides on the basis of our resonator measurements. Suchwaveguides enable the concentration of light to very high optical fieldswithin nano-scale dimensions, and show promise for the confinement oflight in low-index material with potential applications for opticalmodulation, nonlinear optics and optical sensing. As will beappreciated, the precise geometry of a resonator (or other kinds ofdevices) is frequently a matter of design, and the geometry can bevaried based on such considerations as length of waveguide, area of achip, and required interaction (or required non-interaction), such ascoupling (or avoiding coupling) with other waveguide structures that arepresent in a device or on a chip. In some embodiments, the waveguide canbe a closed loop, such as at least one ring or at least one oval shapedendless stripe. As has been explained, optical energy can be provided tosuch a closed loop, for example with an input waveguide.

One can form high quality factor ring or oval resonators in SOI. Inthese SOI waveguides, vertical confinement of light is obtained from theindex contrast between the silicon core and the low index cladding andthe buried silicon dioxide layer, whereas lateral confinement can beobtained by lithographically patterning the silicon. The majority of thelight tends to be guided within the silicon core in such waveguide.Although the high refractive index contrast between silicon and itsoxide provide excellent optical confinement, guiding within the siliconcore can be problematic for some applications. In particular, at veryhigh optical intensities, two-photon absorption in the silicon may leadto high optical losses. Moreover, it is often desirable to maximize thefield intensity overlap between the optical waveguide mode and a lowerindex cladding material when that cladding is optically active andprovides electro-optic modulation or chemical sensing.

One solution to these problems involves using a slot waveguide geometry.In a slot waveguide, two silicon stripes are formed by etching an SOIslab, and are separated by a small distance. In one embodiment, theseparation is approximately 60 nm. The optical mode in such a structuretends to propagate mainly within the center of the waveguide. In thecase of primarily horizontal polarization, the discontinuity conditionat the cladding-silicon interface leads to a large concentration of theoptical field in the slot or trench between the two stripes. One canpredict that the electric field intensity would be approximately 10⁸ √PV/m where P is the input power in watts. FIG. 4 shows the approximategeometry used for the design in this embodiment, as well as the solvedmode pattern for light at approximately 1.53 μm. As seen in FIG. 4, themode profile comprises |E| contours, plotted in increments of 10% of themaximum field value. The E field is oriented primarily parallel to thewafer surface. This mode was obtained from a full vectoral eigensolverbased on a finite difference time domain (FDTD) model. Some embodimentsdescribed herein use a 120 nm silicon on insulator layer and 300 nm wideby 200 nm thick silicon strips on top of a 1.4 μm thick buried oxidelayer, which is in turn deposited on a silicon substrate. After thelithographic waveguide definition process, polymethylmethacrylate (PMMA)was deposited as the top cladding layer. Various widths for the centralslot were fabricated to provide test devices with 50, 60 and 70 nm gaps.The mode profile shown in FIG. 4 and the dispersion diagram shown inFIG. 5 are for a 60 nm slot. FIG. 5 is a diagram showing the effectiveindex vs. free space wavelength in microns for the slot waveguide ofFIG. 4. Slots larger than 70 nm have also been fabricated and were shownto work well. The slot waveguide with a 50 nm slot and 300×200 nm armsfor enhancement of nonlinear moment enjoys an improvement by around afactor of 10 over the effective nonlinearity of simple ridge waveguideshaving a single 500×100 nm Si ridge geometry that are coated with anonlinear polymer cladding.

In the 1.4-1.6 μm wavelength regime, the waveguide geometry is singlemode, and a well-contained optical mode is supported between the twosilicon waveguide slabs. There is some loss that such an optical modewill experience even in the absence of any scattering loss or materialabsorption due to leakage of light into the silicon substrate. Thesubstrate loss can be estimated semi-analytically via perturbationtheory, and ranges from approximately −0.15 dB/cm at 1.49 μm to about−0.6 dB/cm at 1.55 μm for the SOI wafer geometry of the presentembodiment.

Oval resonators were fabricated by patterning the slot waveguides intoan oval shape. An oval resonator geometry was selected in preference tothe more conventional circular shape to enable a longer couplingdistance between the oval and the external coupling waveguide or inputwaveguide. See FIG. 6. Slots were introduced into both the oval andexternal coupling waveguides. FIG. 7 and FIG. 8 show scanning electronmicrograph images of an exemplary resonator and the input coupler.

Predicting coupling strength and waveguide losses for such devices isnot easy. Many different coupling lengths and ring to input waveguideseparations were fabricated and tested. It is well known that the mostdistinct resonance behavior would be observed for critically coupledresonators, in which the coupling strength roughly matches the roundtrip loss in the ring.

An analytic expression for the quality factor of a ring resonator waspresented in equation (1) hereinabove.

Also, the free spectral range can be calculated via:

$\begin{matrix}{{\Delta \; \lambda} = \frac{\lambda^{2}/L}{n - {\lambda \frac{\partial n}{\partial\lambda}}}} & (2)\end{matrix}$

Here, L is the round trip length in the ring, and n₀ and λ₀ are theindex of refraction, and the wavelength at resonance, respectively. Thederivative of the effective index with respect to the wavelength at theresonance peak is given by (δn/δλ)₀, and it can be shown that this termis roughly equal to −0.6 μm⁻¹ from the 1.4-1.6 μm spectral range for theslot waveguides studied here.

We have observed a quality factor of 27,000 in a device fabricated witha slot size of 70 nm, a ring to input waveguide edge to edge separationof 650 nm, and a coupling distance of 1.6 μm. The radius of the circularpart of the slotted oval was 50 μm. This resonance was observed near1488 nm, and the resonance peak had an extinction ratio of 4.5 dB. FIG.9 shows the measured transmission spectrum past the ring, normalized forthe input coupler baseline efficiency of our test system. FIG. 10 showsthe details of one peak in the vicinity of 1488 nm. Because theextinction ratio at the resonance peak was not very large in this case,it was not possible to accurately determine waveguide losses from thisdevice. By measuring many devices with different geometries, we obtaineddata on resonators with higher extinction ratios that approachedcritical coupling. One such device was a 50 μm radius slotted ringresonator with a 60 nm waveguide gap, a ring to input waveguide spacingof 550 nm and coupling length of 1.6 μm. In this device, a Q of 23,400was observed near 1523 nm, with an on-resonance extinction of 14.7 dB.

Since this resonance is nearly critically coupled, the waveguide losscan be estimated using equation (1) as −10 dB/cm. We can also useequation (2) to further validate our theoretical picture of the ringresonator. The observed free spectral range of this resonator was 2.74nm, while equation (2) predicts 2.9 nm. This discrepancy is most likelydue to small differences in the fabricated dimensions as compared tothose for which the numerical solutions were obtained.

To further validate the waveguide loss result, several waveguide losscalibration loops were fabricated with varying lengths of the slotwaveguide, ranging from 200 to 8200 um in length. A total of five centerslot waveguide devices were studied for each of the 50, 60 and 70 nmslot widths. Linear regression analysis on the peak transmission of eachseries yielded waveguide loss figures of 11.6±3.5 dB/cm for the 50 nmcenter waveguide, 7.7±2.3 dB/cm for the 60 nm center waveguide, and8.1±1.1 dB/cm for the 70 nm center waveguide. These figures are inagreement with the loss estimated from the oval resonator. Since thetheoretical loss due to substrate leakage is much lower than this, it isclear that a great deal of loss is due to surface roughness and possiblymaterial absorption. It is believed that engineering improvements willdecrease this loss further. For sensing and modulation applications aswell as use in nonlinear optics, the high optical field concentrationthat can be supported in the cladding material of the slotted waveguidegeometry should be very advantageous when compared to more conventionalwaveguides.

FIG. 11 is a diagram showing a shallow angle SEM view of asilicon-on-insulator ring resonator and waveguide having a sidewallroughness on the order of 10 nm. In the exemplary waveguide shown inFIG. 11, the silicon-insulator bond has been decorated with a briefbuffered oxide etch. FIG. 12 is a diagram of a slot ring resonatordirectional coupler region, and the associated input waveguide.

By comparison, FIG. 13 is a diagram showing a slot waveguide structurethat exhibits subfield stitching errors at the edge of the inputwaveguide in the example shown. Such errors can be devastating forwaveguide loss. Because electric fields are known to concentrate atsharp corners or surface irregularities, it is expected that such sharpfeatures occurring at undefined (or random) locations on the surface ofa waveguide will have deleterious consequences for the desired electricfield profiles. FIG. 14 is yet another example of a rough wall that islikely to create problems in device fabrication and operation. It istherefore preferred that the walls of waveguides according to principlesof the invention be constructed so as to minimize the occurrence ofsharp features.

Other variations on the geometry of waveguides are possible. FIG. 15 isa diagram showing an exemplary high-index segmented waveguidestructures, which in the embodiment shown comprises a central waveguideportion with fingers or ridges sticking out to the sides. With the lightlocalized in the center in a Bloch mode, electrical contact can beestablished using the fingers or ridges that stick off the sides of thewaveguide. This structure provides a way to form both electricalcontacts to waveguides and structures that would provide electricalisolation with low optical loss. Through an iterative process involvinga combination of optical design using a Hermetian Bloch mode eigensolverand fabrication of actual structures, it was found that (non-slotted)segmented waveguide structures could be constructed in 120 nm thick SOI.Waveguide losses as small as −16 dB per centimeter were observed, andinsertion losses as small as −0.16 dB were shown from standard siliconwaveguides.

The segmented waveguide structure can also be modeled as regards itsexpected properties, which can then be compared to actual results. FIG.16A is a diagram that shows a dispersion diagram of both a segmentedwaveguide and the normal, unsegmented waveguide, taken on a planeparallel to the substrate that on a z plane that intersects the middleof a segment. FIG. 16B is a diagram that shows modal patterns of theBloch mode, with contours of |E| plotted, starting at 10% of the maxvalue and with contour increments of 10%. FIG. 16C is a diagram thatshows a plot of modal patterns over four periods of a segmentedwaveguide on a horizontal plane that intersects the silicon layerhalfway through.

By utilizing the same type of design methodology as was used for thesegmented waveguides, one is able to able to construct structures thatprovide electrical isolation without substantial optical loss. FIG. 17is a diagram that shows an exemplary electrical isolator that wasconstructed and tested, and which provided both a transition from astandard to a slotted waveguide and electrical isolation between the twosides of the slot waveguide. Such structures were shown to have losseson the order of 0.5 dB.

Exemplary Results for Waveguides with Cladding Materials Examples 1-4Four-Wave Mixing in Silicon Waveguides with χ3 Polymer Material

Two types of integrated nano-optical silicon waveguide structures wereused for this demonstration. The first type of structure was a series ofring resonator structures, which allowed an estimation of the waveguideloss of the nonlinear material. The second type of structures used waslong runout devices, which comprised a simple waveguide loop withdistances on the order of 0.7 cm. Characterization of loss could be donepassively.

For the actual nonlinear testing, a Keopsys EDFA was used to boost twolasers to a high power level, on the order of 30 dBm (1 Watt) or more.

The materials used for the demonstrations were clad on waveguidesconfigured as previously described herein. The chromophore identified asJSC1 is shown by its chemical structure in FIG. 26. The chromophoresidentified as JSC1 and YLD 124 are two substances among manychromophores that were described in a paper by Alex Jen, et al.,“Exceptional electro-optic properties through molecular design andcontrolled self-assembly,” Proceedings of SPIE—The International Societyfor Optical Engineering (2005), 5935 (Linear and Nonlinear Optics ofOrganic Materials V), 593506/1-593506/13. The paper describes at leastfive additional specific chromophores, and states in part that a “seriesof guest-host polymers furnished with high μβ chromophores have shownlarge electro-optic coefficients around 100˜160 pm/V @ 1.31 μm.” It isbelieved that the several examples given in the present descriptionrepresent a few specific examples of many chromophores that can be usedas materials having large nonlinear coefficients χ2 and χ3 according toprinciples of the systems and methods disclosed herein. Four types ofcladdings were applied to waveguides situated on silicon dies:

1. JSC1/APC: The chromophore JSC1 is doped into amorphous polycarbonate(APC) with the loading of 35 wt %. The solvent we used is cyclohexanone,and concentration of overall solid in this solution is 14 wt %.2. AJL21/PMMA: The chromophore AJL21 is doped into PMMA with the loadingof 40 wt %. The solvent used was 1,1,2-trichloroethane, and solutionconcentration was 10 wt %.3. AJL21 monolithic films: The chromophore AJL21 is coated by itselfmonolithically. The solvent was 1,1,2 trichloroethane, and theconcentration was 10 wt %.4. AJC212 monolithic films: The chromophore AJC212 was coated by itselfmonolithically. The solvent was cyclopentanone, and concentration was 11wt %. This film may have wetting problems, as evidenced by peripheryshrinkage after baking.

Passive Results

Waveguide loss was measured for each of the four die. Intrinsicwaveguide loss with a cladding having an index of 1.46 is about 7 dB/cm.A cladding with n>1.46 would lower this figure slightly. The total lossand the estimated loss due to the polymer are presented separately. Thisis based on subtracting 7 dB from the polymer, and then multiplying bythree, because the polymer causes approximately as third as much loss asit would for the mode if it were in a bulk material, because not all ofthe optical energy interacts with the polymer.

Die 1: 30 dB/cm; 69 dB/cm for bulk polymerDie 2: 5.7 dB/cm; <1 dB/cm for bulk polymerDie 3: the loss was too high to measure devicesDie 4: 10 dB/cm; 12 dB/cm for bulk polymer

Active Results

The intrinsic nonlinear response of our EDFA and optical test system wasmeasured to determine a baseline for measurements on devices. FIG. 18 isa diagram showing the results of a baseline measurement of an EDFA andoptical test system in the absence of a test sample. As can be seen inFIG. 18, there is a very small amount of four wave mixing that occurs.This test was performed with about 28 dBm of EDFA output. There is 40 dBof extinction from the peak to the sidebands.

A Die 1 loop device with 7000 μm of runlength produced about 29 dB ofconversion efficiency (that is, sidebands were 29 dB down from peak atend of run).

FIG. 19 is a diagram showing the results for the measurement of a firstexemplary material having a large value of χ³, namely Die 1 with acladding. Even though the plot looks similar to that shown in FIG. 18,in fact there is an order of magnitude more nonlinear conversion thathas occurred. The insertion loss is due to the grating couplers and thewaveguide loss in the device.

FIG. 20 is a diagram showing the results for the measurement of a firstexemplary material having a large value of χ³, namely Die 2 with acladding, which showed better results than Die 1. Here there is about 20dB of extinction from the right peak to the left sideband, and 22 dBfrom the larger peak on the left to the left sideband. This is theresult that represents a demonstration of 1% conversion efficiency.

The noise level on some of these scans is higher than others becausesome were taken with faster scan settings on the optical signalanalyzer.

Semi-Analytic Results

The slowly varying approximation can be used to generate thecharacteristic equations to predict the conversion efficiency. Leta0(z), a1(z) and a2(z) be the amplitudes of the 3 wavelengths involvedin a given .four-wave mixing interaction. Let w2=2*w0−w1. Approximately,E is 10⁸ V/m for 1 Watt of power. so if we take E=a0(z)*10⁸ V/m then a0is power normalized to be 1 watt when |a0|=1. The characteristicequations are:

$\begin{matrix}{{\frac{\partial a_{0}}{\partial z} = {6f\frac{\; \beta_{0}}{{neff}_{0}^{2}}{\exp ( {( {{{- 2}\; \beta_{0}} + \beta_{1} + \beta_{2}} )\; z} )}a\; 0*a\; 1\; a\; 2}}{\frac{\partial a_{1}}{\partial z} = {{3f\frac{{\beta}_{1}}{{neff}_{1}^{2}}{\exp ( {( {{2\; \beta_{0}} - \beta_{1} - \beta_{2}} )\; z} )}a\; 0a\; 0a\; 2*\frac{\partial a_{2}}{\partial z}} = {3f\frac{\; \beta_{2}}{{neff}_{2}^{2}}{\exp ( {( {{2\; \beta_{0}} + \beta_{1} + \beta_{2}} )\; z} )}a\; 0a\; 0a\; 1*}}}} & (3)\end{matrix}$

The quantity f is taken as an unknown fraction which reduces the effectof the nonlinear material due to the fact that some of the opticalenergy is not in the optical region, but in the waveguide core. It isestimated that f is about 0.1, with an uncertainty of perhaps a factorof 2.

The phasor factor turns out to have an oscillation period on the orderof a meter for the waveguides under consideration, and can be ignored.Based on a numerical integration, one can then estimate the χ3coefficients for die 1 and die 2 as:

Die 1: χ3 is nearly 8×10⁻²² (m/V)2Die 2: χ3 is approximately 1.5⁻²² (m/V)2

FIG. 21 is a diagram that shows a plot of the numerically computedconversion efficiency for Die 2, in dB vs 1 watt compared to lengthtraveled in waveguide in μm.

The devices that were tested were observed in all cases to eventuallyfail, either when ramping up the power levels or after extended testing.It is believed that the problem is caused by heating damage. Fortunatelythe damage seems not to extend to the silicon waveguides. This meansthat devices that fail in this way can be recovered by stripping thepolymers, and then being recoated. With additional experience, solutionsfor the problem of this damage problem may be identified and solved.

It is unfortunate that the waveguide loss in the die 1 material is sohigh, because it is a material that exhibits extremely high χ3.Nevertheless, reasonable efficiencies were demonstrated with materialexhibiting a lower χ3. It would be advantageous to identify a materialwith a value of χ3 that is larger by a factor of 10 or so. It would alsobe advantageous to lower the waveguide loss slightly. With these twoadjustments, it would be possible to enter the “strong coupling” regime,so that one might observe 100% conversion in lengths <0.5 cm. One likelypossibility would be to lower the optical loss of the Die 1 material,JSC1.

Example 5 Optical Modulation and Detection in Slotted Silicon Waveguides

In some embodiments, an optical input signal can be directly convertedto an electrical output signal via a process known as opticalrectification. This process occurs when a particularly intense opticalbeam is incident on a χ2 material, and induces a low frequency electricfield as a result. The large magnitude of this electric field is due tothe enhancement of the optical field in a slot waveguide. This processhas many advantages over conventional detection schemes, such asphotodiodes. In particular, there will be nearly no speed limit for thistype of detector, because the mechanism is ultrafast and functions atthe optical frequency.

In this example, we describe a system and process that provide low poweroptical detection and modulation in a slotted waveguide geometry filledwith nonlinear electro-optic polymers and present examples thatdemonstrate such methods. The nanoscale confinement of the optical mode,combined with its close proximity to electrical contacts, enables thedirect conversion of optical energy to electrical energy, withoutexternal bias, via optical rectification, and also enhanceselectro-optic modulation. We demonstrate this process for power levelsin the sub-milliwatt regime, as compared to the kilowatt regime in whichoptical nonlinear effects are typically observed at short length scales.The results presented show that a new class of detectors based onnonlinear optics can be fabricated and operated.

Waveguide-based integrated optics in silicon provide systems and methodsfor concentrating and guiding light at the nanoscale. The high indexcontrast between silicon and common cladding materials enables extremelycompact waveguides with very high mode field concentrations, and allowsthe use of established CMOS fabrication techniques to define photonicintegrated circuits. As we have already explained hereinabove, by usingslotted waveguides, it is possible to further concentrate a largefraction of the guided mode into a gap within the center of a siliconwaveguide. This geometry greatly magnifies the electric field associatedwith the optical mode, resulting in electric fields of at least (or inexcess of) 10⁶ V/m for continuous-wave, sub-milliwatt optical signals.Moreover, since the slotted geometry comprises two silicon strips whichcan be electrically isolated, a convenient mechanism for electro-opticinteraction is provided. Such waveguides can be fabricated with lowloss. We have previously described systems that provide losses below −10dB/cm.

In the present example, we exploit both the high intensity of theoptical field and the close proximity of the electrodes for severalpurposes. First, we demonstrate detection of optical signals via directconversion to electrical energy by means of nonlinear opticalrectification. An exemplary device comprises a ring resonator with anelectro-optic polymer based χ² material deposited as a cladding. Insidethe slot, the high optical field intensity creates a standing DC field,which creates a virtual voltage source between the two siliconelectrodes, resulting in a measurable current flow, in the absence ofany external electrical bias. Though optical rectification has beenobserved in electro-optic polymers, typically instantaneous opticalpowers on the order of 1 kW are needed for observable conversionefficiencies, often achieved with pulsed lasers. The exemplaryembodiment provides measurable conversion with less than 1 mW ofnon-pulsed input, obtained from a standard, low power tunable laseroperating near 1500 nm.

In one embodiment, systems and methods of the invention provide standardPockels effect based modulation, which is similarly enhanced by means ofthe very small scale of our device. The close proximity of theelectrodes, and ready overlap with the optical mode, causes an externalvoltage to produce a far larger effective electric modulation field, andtherefore refractive index shift, than would be obtained throughconventional waveguide designs. In one embodiment, the modulation andrefractive index shift is provided by tuning the resonance frequenciesof a slot waveguide ring resonator.

Device Fabrication Waveguide Fabrication

The devices described in this example were fabricated in electronicgrade silicon-on-insulator (SOI) with a top layer thickness of 110 nmand an oxide thickness of 1.3 microns. The silicon layer is subsequentlydoped to approximately 10¹⁹ Phosphorous atoms/cm³, yieldingresistivities after dopant activation of about 0.025 ohm-cm.Electro-optic (“EO”) polymers were then spin-deposited onto thewaveguide structures and subsequently poled by using a high fieldapplied across the slot in the waveguide.

Lithography was performed using a Leica EBPG 5000+ electron beam systemat 100 kv. Prior to lithography, the samples were manually cleaved,cleaned in acetone and isopropanol, baked for 20 minutes at 180 C,coated with 2 percent HSQ resist from Dow Corning Corporation, spun fortwo minutes at 1000 rpm, and baked for an additional 20 minutes. Thesamples were exposed at 5 nm step size, at 3500 μC/cm². The samples weredeveloped in AZ 300 TMAH developer for 3 minutes, and etched on anOxford Instruments PLC Plasmalab 100 with chlorine at 80 sccm, forwardpower at 50 W, ICP power at 800 W, 12 mTorr pressure, and 33 seconds ofetch time. The samples were then implanted with phosphorous at normalincidence, 30 keV energy, and 1×10¹⁴ ions/cm² density. The sample wasannealed under a vacuum at 950 C in a Jipilec Jetstar rapid thermalannealer. The samples were dipped in buffered hydrofluoric acid in orderto remove the remnants of electron beam resist from the surface.

After initial optical testing, the samples were coated with YLD 124electro-optic polymer, and in one case with dendrimer-basedelectro-optic material. The samples were stored under a vacuum at alltimes when they were not being tested, in order to reduce the chances ofany degradation.

Synthesis of YLD 124 Coating Solution

FIG. 22 is a diagram showing a chemical reaction useful for thesynthesis of a chromophore referred to as YLD 124. The compound denotedin FIG. 22 by 1 is discussed in the paper by C. Zhang, L. R. Dalton, M.C. Oh, H. Zhang, W. H. Steier, entitled “Low V-pi electro-opticmodulators from CLD-1: Chromophore design and synthesis, materialprocessing, and characterization,” which was published in Chem. Mater.,volume 13, pages 3043-3050 (2001).

To a solution of 0.56 g (0.96 mmol) of 1 and 0.36 g of 2 (1.1 mmol) in1.5 mL of THF was added 6 mL of absolute ethanol. The mixture wasstirred for 6 h at room temperature. The precipitate was collected byfiltration and washed by ethanol and methanol. The crude product wasdissolved in minimum amount of CH₂CI₂. The resultant solution was addeddropwisely to 100 mL of methanol. The product (0.76 g) was collected asdark green precipitate. Yield was 90%. ¹H NMR (CDCl₃): 8.05 (t, J=13.6Hz, IH), 7.45-7.58 (m, 5H), 7.38 (d, J=8.9 Hz, 2H) 6.93 (d, J=15.9 Hz,IH) 6.79 (d, J=15.9 Hz, 1H), 6.70 (d, J=8.9 Hz, 2H), 6.40-6.25 (m, 3H),3.80 (t, J=5.8 Hz, 4H), 3.59 (t, J=5.8 Hz, 4H), 2.42 (s, 2H), 2.40 (s,2H), 1.04 (s, 3H), 0.98 (s, 311), 0.90 (s, 18H), 0.04 (5, 12H). MS(ESP): 879.48 (M+H). UV-Vis (THF): 765 nm. m.p. 173° C.

One part of YLD 124 was mixed with three parts of APC (Poly[Bisphenol Acarbonate-co-4,4′-(3,3,5-trimethylcyclohexylidene)diphenol carbonate]).The mixture was dissolved in cyclopentanone. The total solid content(YLD 124 and APC) is about 12%. The resultant solution was filteredthrough a 0.2 pm filter before being used on the device to provide acladding layer comprising the chromophore YLD 124.

Measurement Results Optical Rectification Based Detection

FIG. 23 is a four panel diagram that shows details of one embodiment ofan optical modulator device, including the geometry of thephotodetectors and filters, and including a cross section of the slottedwaveguide. Panel A of FIG. 23 shows a cross section of the devicegeometry with optical mode superimposed on a waveguide. In FIG. 23(A),the optical mode was solved using a finite-difference based HermetianEigensolver, such as that described by A. Taflove, ComputationalElectrodynamics, (Artech House, Boston. MA, 1995), and has an effectiveindex of approximately 1.85 at 1500 nm. Most of the electric field isparallel to the plane of the chip, and it is possible to contact bothsides of the slot in a slotted ring resonator, as shown in FIG. 23(B).Panel B of FIG. 23 shows a SEM image of the resonator electricalcontacts. Electrically isolated contacts between the silicon railsdefining the slotted waveguide introduce only about 0.1 dB of opticalloss. Panel C of FIG. 23 shows the logical layout of device,superimposed on a SEM image of a device. FIG. 23(C) details the layoutof a complete slotted ring resonator, with two contact pads connected tothe outer half of the ring, and two pads electrically connected to theinner half of the ring. A shunt resistor provides a means of confirmingelectrical contact, and typical pad-to-pad and pad-to-ring resistancesrange from 1MΩ to 5MΩ. FIG. 23(D) displays a typical electricallycontacted slotted ring described in this study. Panel D of FIG. 23 is animage of the ring and the electrical contact structures.

Measurements were performed with single-mode polarization maintaininginput and output fibers, grating coupled to slotted waveguides with aninsertion loss of approximately 8 dB. Optical signal was provided froman Agilent 81680a tunable laser and in some cases an erbium doped fiberamplifier (“EDFA”) from Keopsys Corporation. A continuous optical signalinserted into a poled polymer ring results in a measurable currentestablished between the two pads, which are electrically connectedthrough a pico-Ammeter. In the most sensitive device, a DC current of˜1.3 nA was observed, indicating an electrical output power of ˜10⁻⁹ ofthe optical input power (5×10⁻¹² W of output for approximately 0.5 mWcoupled into the chip). Control devices, in which PMMA or un-poled EOmaterial was substituted, show no photocurrent.

The fact that there is no external bias (or indeed any energy source)other than the optical signal applied to the system of this embodimentdemonstrates conclusively that power is being converted from the opticalsignal. To establish that the conversion mechanism is actually opticalrectification, we performed a number of additional measurements. Asteady bias was applied to the chip for several minutes, as shown inTable 1A. A substantial change in the photoresponse of the device wasobserved. This change depends on the polarity of the bias voltage,consistent with the expected influence of repoling of the devicein-place at room temperature. Specifically, if the external bias wasapplied opposing the original poling direction, conversion efficiencygenerally decreased, while an external bias in the direction of theoriginal poling field increased conversion efficiency.

In the present invention, we understand that an optical material can besubject to spatially periodic repoling of the electrooptic material, forexample to provide a particular functionality, such as a nonlinear orexponential functionality or behavior.

TABLE I Poling Results Part A: Action New Steady State Current (6 dBminput) Initial State −5.7 pA +10 V for 2 minutes     0 pA −10 V for 2minutes −7.1 pA +10 V for 2 minutes −4.4 pA +10 V for 4 minutes −6.1 pA−10 V for 4 minutes −4.5 pA −10 V for 2 minutes −14.8 pA  Part B:Current Polarity of Device Action Optical Rectification 1 PositivePoling Positive 1 Thermal Cycling to Rapid fluctuation, did polingtemperature with not settle no voltage 1 Negative Poling Negative 2Negative Poling Negative 2 Thermal Cycling to None observable Polingtemperature with no voltage 2 Positive Poling Negative 3 Negative PolingNegative 4 Positive Poling Positive 5 Negative Poling Negative

To further understand the photo-conversion mechanism, 5 EO detectiondevices were poled with both positive and negative polarities, thusreversing the direction of the relative χ² tensors. For these materials,the direction of χ² is known to align with the polling E fielddirection, and we have verified this through Pockels' effectmeasurements. In all but one case, we observe that the polarity of thegenerated potential is the same as that used in poling, and the +Vterminal during poling acts as the −V terminal in spontaneous currentgeneration, as shown in Table 1B. Furthermore, the polarity of thecurrent is consistent with a virtual voltage source induced throughoptical rectification. It was observed that these devices decaysignificantly over the course of testing, and that in one case thepolarity of the output current was even observed to spontaneously switchafter extensive testing. However, the initial behavior of the devicesafter polling seems largely correlated to the χ² direction.

Part A of Table I shows the dependence of the steady state observedcurrent after room temperature biasing with various voltage polaritiesfor one device. The device was originally polled with a ˜12 V bias,though at 110 C. With one exception, applying a voltage in the directionof the original polling voltage enhances current conversionefficiencies, while applying a voltage against the direction of thepolling voltage reduces the current conversion efficiencies. It shouldbe noted that the power coupled on-chip in these measurements was lessthan 1 mW due to coupler loss.

Part B of Table I shows the behavior of several different devicesimmediately after thermal polling or cycling without voltage.Measurements were taken sequentially from top to bottom for a givendevice. The only anomaly is the third measurement on device 2; this wasafter significant testing, and the current observed was substantiallyless than was observed in previous tests on the same device. We suspectthat the polymer was degraded by repeated testing in this case.

A number of measurements were performed to attempt to produce negativeresults, and to exclude the possibility of a mistaken measurement ofphotocurrent. The power input to the chip was turned on and off bysimply moving the fiber array away from the chip mechanically, withoutchanging the circuit electrically, and the expected change in theelectrical output signal of our detector was observed. A chip was coatedin polymethylmethacrylate and tested, resulting in no observedphotocurrents. Also, when some of the devices shown in Table I weretested before any polling had been performed; no current was observed.

We used a lock-in amplifier to establish a quantitative relationshipbetween the laser power in the EQ material and the photo-current, andachieved a noise floor of about 0.2 pA. This resulted in a reasonabledynamic range for the 10-200 pA photocurrent readings. FIG. 24(A) andFIG. 24(B) show optical transmission curves for typical devices. FIG.24(C) shows several traces of output current versus input laser power,and a fairly linear relationship is observed. The relationship I=cP,where I is the output current, P is the input laser power, and c is aproportionality constant ranging from 88+/−10 pA/mW at a 1 kHz lock-inmeasurement and when the wavelength is on resonance, changing to a lowervalue of 58+/−8 pA/mW off resonance for the best device. It is importantto note that current was easily observed with only a pico-ammeter, or bysimply connecting an oscilloscope to the output terminal and observingthe voltage deflection.

Panel A of FIG. 24 shows the transmission spectrum of detector device I.Panel B of FIG. 24 shows the transmission spectrum of detector device 2.Panel C of FIG. 24 shows several curves of current vs. power for threemeasurement series. Series 1 is of the first device with the wavelengthat 1549.26 nm, on a resonance peak. Series 2 is the first device withthe wavelength at 1550.5 nm off resonance. Series 3 is for device 2,with the wavelength at 1551.3 nm, on resonance. Finally, panel D of FIG.24 shows the output current as a function of wavelength, overlaid withthe transmission spectrum. The transmission spectrum has beenarbitrarily rescaled to show the contrast.

As another demonstration of the dependence of the output current on theamount of light coupled into the resonator, we also tuned the laserfrequency and measured the output current. As can be seen in FIG. 24(D),the amount of output current increases as the laser is tuned onto aresonance peak. This again indicates that the overlap between the EOpolymer in the resonator and the optical mode is responsible for thephoto-current. We have overlaid a photocurrent vs. wavelength responsescan to show the resonance peaks for comparison. It should not besurprising that a small photocurrent is still measured when the laser isoff resonance, since the amount of radiation in a low-Q ring resonatoris non-negligible oven off resonance. We have successfully observed thisdetector function at speeds up to 1 MHz, without significant observablerolloff. This is again consistent with optical rectification.Unfortunately, our devices could not be measured at higher speeds, dueto substantial output impedance.

The conversion efficiency from our first measurements is thought to beseveral orders of magnitude below the ultimate limit, and can beexplained by the high insertion losses in our system. In the presentembodiment, 75% of the input power in the fiber is not coupled onto thechip. Our low-Q resonators only provide a limited path length withinwhich light can interact with the electro-optic material. Furthermore,by design a great deal of the light in the resonator will be dumped toan output port, and not absorbed. It is expected that with furtherdesign and higher Q resonators, the efficiency of these devices can begreatly increased. It is, however, important to note that nothing aboutthis effect depends on the presence of rings. The rings provide aconvenient and compact device for observing these effects, but one couldjust as easily observe optical rectification by using other geometries,such as a long linear, polymer coated, split waveguide, with each sideconnected to an electrical pad.

Pockels' Effect Modulation

At DC, the Pockels effect was measured by applying varying voltages tothe device and observing the device transmission as a function ofwavelength. For devices having operative modulation, the resonance peakswere shifted, often to a noticeable degree. To counter the systemicdrift due to temperature fluctuations, a series of random voltages wereapplied to a device under test and the wavelength responses noted. Theintersection of a resonance peak and a certain extinction, chosen to beat least 10 dB above the noise floor, was followed across multiplescans. A 2d linear regression was performed, resulting in twocoefficients, one relating drift to time, and one relating drift tovoltage.

At AC, a square wave input voltage was applied across the device. Theinput wavelength was tuned until the output signal had the maximumextinction. It was determined what power levels were implied by theoutput voltage, and then the observed power levels were fit to awavelength sweep of the resonance peak. This readily allowed the tuningrange to be calculated. We successfully measured AC tuning up to the lowMHz regime. The limitation at these frequencies was noise in ourelectrical driving signal path, and not, as far as we can tell, anyrolloff in the modulation process itself.

FIG. 25 is a diagram showing the use of the structures embodying theinvention as resonantly enhanced electro-optic modulators, and a resultat approximately 6 MHz operating frequency, representing a bit patterngenerated by Pockels' Effect modulation of 5 dB. The vertical axisrepresents input voltage and output power, both in arbitrary units. Thehorizontal axis represents time in units of microseconds. Voltage swingon the input signal is 20 volts. These measurements clearly demonstratethat low-voltage electro-optic tuning and modulation can be achieved inthe same geometries as have been described for photodetection. It shouldbe emphasized that these devices are not optimized as modulators. Byincreasing the Q of the resonators to exceed 20,000, which has beendescribed hereinabove, it will be possible to achieve much largerextinction values per applied voltage.

By utilizing new dendrimer-based electro-optic materials, we haveachieved 0.042±008 nm/V_(π) or 5.2±1 GHz/V for these rings. This impliesan r₃₃ of 79±15 pm/V. This result is better than those obtained forrings of 750 micron radius, which we believe to be the best tuningfigure published to date. By contrast, our rings have radii of 40microns. We credit our improvement over the previous results mainly tothe field enhancement properties of our waveguide geometry.

Additional Results

Optical modulators are a fundamental component of optical datatransmission systems. They are used to convert electrical voltage intoamplitude modulation of an optical carrier frequency, and they can serveas the gateway from the electrical to the optical domain. High-bandwidthoptical signals can be transmitted through optical fibers with low lossand low latency. All practical high-speed modulators that are in usetoday require input voltage shifts on the order of 1V to obtain fullextinction. However it is extremely advantageous in terms of noiseperformance for modulators to operate at lower drive voltages. Manysensors and antennas generate only millivolts or less. As a result it isoften necessary to include an amplifier in optical transmission systems,which often limits system performance. By using silicon nano-slotwaveguide designs and optical polymers, it is possible today toconstruct millivolt-scale, broadband modulators. In some embodiments, amillivolt-scale signal is one having a magnitude of hundreds ofmillivolts. In some embodiments, a millivolt-scale signal is one havinga magnitude of tens of millivolts. In some embodiments, amillivolt-scale signal is one having a magnitude of units of millivolts.Using novel nanostructured waveguide designs, we have demonstrated a100× improvement in Vπ over conventional electro-optic polymermodulators.

A variety of physical effects are available to produce opticalmodulation, including the acousto-optic effect, the Pockels effecteither in hard materials, such as lithium niobate or in electro-opticpolymers, free-carrier or plasma effects, electro-absorption, andthermal modulation. For many types of optical modulation, the basicdesign of a modulator is similar; a region of waveguide on one arm of aMach-Zehnder interferometer is made to include an active opticalmaterial that changes index in response to an external signal. Thismight be, for instance, a waveguide of lithium niobate, or asemiconductor waveguide in silicon. In both cases, a voltage isintroduced to the waveguide region by means of external electrodes. Thiscauses the active region to shift in index slightly, causing a phasedelay on the light traveling down one arm of the modulator. When thelight in that arm is recombined with light that traveled down areference arm, the phase difference between the two signals causes thecombined signal to change in amplitude, with this change depending onthe amount of phase delay induced on the phase modulation arm. Otherschemes, where both arms are modulated in order to improve performance,are also common.

The measure of the strength of a modulation effect is how much phaseshift is obtained for a given input voltage. Typical conventionalmodulators obtain effective index shifts on the order of 0.004% for 1 V.This implies that a Mach-Zehnder 1 cm in length, meant to modulateradiation near 1550 nm, would require 1 V of external input for the armsto accumulate a relative phase shift of π radians. The half wave voltageV_(π) (or V_(pi)) is the voltage needed for an interarm phase shift of πradians (or 180 degrees). Lower values for V_(π) imply that less poweris needed to operate the modulator. Often, the responsivity, alength-independent product V_(π)-L is reported. Typical V_(π)-L valuesare in the range of 8 Vcm in silicon, or 6 V-cm for lithium niobatemodulators. This voltage-length product, or responsivity, is animportant figure of merit for examining a novel modulator design. Makinga modulator physically longer generally trades lower halfwave voltageagainst reduced operating frequency and higher loss. Because generatinghigh-speed and high-power signals requires specialized amplifiers,particularly if broadband performance is required, lowering theoperating voltage of modulators is extremely desirable, particularly foron-chip integrated electronic/photonic applications, (includingchip-to-chip interconnects) where on-chip voltages are limited to levelsavailable in CMOS. FIG. 27 shows a diagram of a Mach-Zehnder modulatorwith a conventional electrode geometry.

FIG. 27 is a top-down view of a simple conventional Mach-Zehnder polymerinterferometer, showing top contact, waveguide, and bottom contactlayers. Such a device is usually operated in ‘push/pull’ mode, whereeither opposite voltages are applied to the different arms, or where thetwo arms are poled in opposite directions to achieve the same effect.

In the past several years, silicon has gained attention as an idealoptical material for integrated optics, in particular attelecommunications wavelengths. Low loss optical devices have beenbuilt, and modulation obtained through free carrier effects. One of thewaveguides that can be supported by silicon is the so-called slotwaveguide geometry. This involves two ridges of silicon placed close toeach other, with a small gap between them. As shown above with regard toFIGS. 23, 24 and 25, we have demonstrated modulation regions based onfilling this gap with a nonlinear material, and using the two waveguidehalves as electrodes. In such a geometry, the silicon is doped to alevel that allows electrical conductivity without causing substantialoptical losses. This allows the two wires or ridges to serve both astransparent electrical contacts and as an optical waveguide.

Using slot waveguides, we previously obtained an improvement inmodulation strength of nearly 5× when compared to the best contemporaryconventional waveguide geometries with electrodes separated from thewaveguide, with the initial, non-optimized designs. This improvement wasbased on the remarkably small width of the gap across which the drivingvoltage drops. It is expected that smaller gaps translate into higherfield per Volt, and the Pockels Effect depends on the local strength ofthe electric field. The smaller the gap, the larger the index shift. Aunique property of slot waveguides is that, even as these gaps becomenanoscale, the divergence conditions on the electric field require thatmuch of the optical mode remains within the central gap. As a result,changing the index within a nanoscale gap can give a remarkably largechange in the waveguide effective index. Because of these divergenceconditions, the optical mode's effective index is largely determined bythe shift found even in very small gaps.

Low V_(π) Modulators

Several major approaches toward achieving low V_(π) modulation haverecently been pursued. The free-carrier dispersion effect in siliconwaveguides has been used. Green et al. achieved a V_(π) of 1.8 V withthis effect. Modulators based on lithium niobate are also frequentlyused. Typical commercially obtained V_(π) values are 4 V. Recently,Mathine and co-workers have demonstrated a nonlinear polymer basedmodulator with a V_(π) of 0.65 V. For the devices produced by others,the attained values of V_(π) are large.

A number of approaches have been proposed for developing low V_(π)modulators. Different proposed approaches rely on the development of newelectrooptic materials, or on optical designs that trade bandwidth forsensitivity, either through the use of resonant enhancement, or throughdispersion engineering. The designs presented herein are based uponconventional, high-bandwidth Mach-Zehnder traveling wave approaches, butachieve appreciable benefits from using nano-slot waveguides. Of course,these designs can also take advantage of the newest and bestelectrooptic polymers. In principle, any material that can be coatedconformally onto the surface of the silicon waveguides and that isreasonably resistive could be used to provide modulation in thesesystems, making the system extremely general.

FIG. 28 is an isometric three dimensional schematic of a conventionalMach-Zehnder polymer interferometer, showing top contact, waveguide, andbottom contact layers. Such a device is usually operated in ‘push/pull’mode, where either opposite voltages are applied to the different arms,or where the two arms are poled in opposite directions to achieve thesame effect.

FIG. 29 is a three dimensional, isometric schematic of a slot-waveguidemodulator, showing the slot waveguide, segmentation region and metalcontacts. The device illustrated in FIG. 29 functions by maintaining thetwo arms of the slot waveguide at differing voltages, creating a strongelectric field in the slot.

FIG. 30 is a top-down view of a layout of a slot-waveguide based opticalmodulator of the device in FIG. 29.

The nonlinear polymers that have been used with slot waveguides exhibita local anisotropic shift in their dielectric constant when they areexposed to an electric field. This is characterized by r₃₃, which is acomponent of the electro-optic tensor. A simplification is appropriateto the case of slot waveguides, where the poling field, the modulationfield, and the optical electric field are all nearly parallel. In thiscase, r₃₃ is defined as:

$\begin{matrix}{{\frac{1}{( {n + {\delta \; n}} )^{2}} - \frac{1}{n^{2}}} = {r_{33}E_{dc}}} & ( {4a} )\end{matrix}$

That is, a shift in the bulk index for this particular polarization isdefined as a product of r₃₃ and the modulating electric field.

We have developed an analytic model to express the modulation strengththat will be observed in a given slot waveguide geometry. Assuming thata nonlinear electro-optic polymer is used, the local shift in dielectricconstant can be expressed as Eqn. (4b):

δ∈=|E _(dc) |vv′(n ⁴ r ₃₃)  (4b)

Here v is the unit vector of the direction of the dc electric field, andn is the bulk refractive index of the nonlinear polymer. Note that δ∈ isa second rank tensor in Eqn. (4b). It has been assumed that the polingdc field is identical to the modulation dc field. Nonlinear polymershave become increasingly strong in recent years, with some of the mostrecently developed material having an r₃₃ of 500 pm/V. This correspondsto an on axis χ² moment of 4.2×10⁻⁹ m/V.

With the optical mode known, the shift in effective index is given byEqn. (5):

$\begin{matrix}{\frac{\partial n}{\partial V} = {\gamma ( {n^{4}r_{33}} )}} & (5)\end{matrix}$

The key parameter for any waveguide involving a nonlinear electro-opticmaterial is γ, which we term the effective index susceptibility. γ isindependent of the nonlinear material properties, and depends only onthe waveguide geometry, and is given by Eqn. (6):

$\begin{matrix}{\gamma = {\frac{\int{{{E_{opt} \cdot v}}^{2}ɛ_{0}{{w( {E_{dc} \cdot v} )}/V}{A}}}{\int{2{{Re}( {{{Ex}_{opt}^{*}{Hy}_{opt}} - {{Ey}_{opt}^{*}{Hx}_{opt}}} )}{A}}}\frac{1}{k_{0}}}} & (6)\end{matrix}$

The ultimate V_(π) that can be obtained is inversely proportional to γ.It is noteworthy that this model accurately predicts Steier et al.'sresults, as shown described below.

For a conventional all-polymer geometry with electrodes external to thewaveguide, γ is 0.026 μm⁻¹. For the slot waveguide that we used in ourprevious experiments, γ was 0.4 μm⁻¹. Finally, for a more optimaldesign, shown in FIG. 33, has a γ of 2.3 μm⁻¹. This design comprises a200 nm thick silicon-on-insulator layer on a silicon dioxide substratethat is etched to create arms with widths of 200 nm with a 20 nm gapbetween them, which is described in more detail as design #3 presentedin Table 2 below. This geometry enjoys an increase of about a factor of100 in the tuning sensitivity compared to the conventional electrodegeometry; this corresponds to a decrease by a factor of 100 in the Vπneeded for modulation. These numbers assume a minimum lithographiclinewidth of 20 nm, which is easily achievable today with electron beamlithography. Narrower linewidths are expected to further improve theachievable performance.

FIG. 31A and FIG. 31B show a conventional electrode geometry for anonlinear polymer waveguide described by Tazawa and Steier (H. Tazawa,Y. Kuo, I. Dunayevskiy, J. Luo, A. K. Y. Jen, H. Fetterman and W.Steier, “Ring resonator based electrooptic polymer traveling-wavemodulator,” IEEE J. Lightwave Technol. 24, 3514-3519 (2006) and Tazawa,H. & Steier, W. H., “Analysis of ring resonator-based traveling-wavemodulators,” IEEE Photonics Technology Letters 18, 211-213 (2006)). FIG.31A shows the optical mode with |E| plotted in increments of 10%, for amode with propagating power of 1 Watt. FIG. 31B shows a contour plot ofthe static electric field, with the field of view slightly enlarged.FIG. 31C and FIG. 31D show analogous data for an improved slot waveguidegeometry according to the present invention. In the slot waveguide, thesilicon provides both the optical guiding layer and the electricalcontacts.

The most recent nonlinear polymers achieve a high nonlinear coefficient,expressed as an r₃₃ of 500 pm/V. Using this in combination with the highsusceptibilities described above, it is believed that it is possibletoday to construct a 1 cm Mach-Zehnder modulator with a V_(π) of 8 mV.This corresponds to a ring resonator with a tuning sensitivity of 795GHz/V. Both of these values are two orders of magnitude better than theperformance obtained by current approaches. Current commerciallyavailable modulators typically have Vπ's from 1 to 9 V, and currenttunable electro-optic polymer based resonators achieve 1 GHz/V oftunability. If the r₃₃ value of 33 pm/V demonstrated by Tazawa andSteier for conventional polymer designs is used, then a V_(π) of 64 mVand a resonator tunability of 50 GHz/V are obtained.

Segmented waveguide contact structures can be formed that allow very lowresistance electrical contact to slot waveguides. We have describedabove, in similar circumstances, electrical contact to waveguides can beestablished via segmented waveguides. See FIG. 23B and FIG. 23D and thediscussion related thereto. When the RC circuits implied by thesegmentation geometry and the gap are examined, it is found that RC turnon times on the order of 200 GHz or more are achievable. Because thenonlinear polymers exhibit an ultrafast nonlinearity, these waveguidegeometries present a path to making Terahertz scale optical modulators.Because the modulation is so strong, it is also possible to trade thelength of the modulator against V_(π). For example, our optimal geometryis expected obtain a Vπ of 0.6 V with a 100 μm long Mach-Zehndermodulator. This device is expected be exceptionally simple to design for10 GHz operation, as it could likely be treated as a lumped element. Wehave shown above that lateral contact structures with low loss and lowresistance can be constructed with these slot waveguides. See FIG. 23Band FIG. 23D and the discussion related thereto.

We believe these nano-slot waveguide designs present a path to realizingvery high speed, low voltage modulators. It is advantageous to be ableto attain a responsivity V_(π)-L of less than 1 V-cm. The physicalprinciples involved in such devices are based on employing a nonlinearmaterial of at least moderate resistivity, and a high index contrastwaveguide with tight lithographic tolerances. Therefore, it is expectedthat nano-slot waveguides, either as Mach-Zehnder or ring-based devices,are likely an advantageous geometry for optical modulation withnonlinear materials in many situations. In addition, materialscompatibility and processing issues are greatly reduced for such devicescompared to conventional multilayer patterned polymer modulatorstructures.

These high index contrast devices have (or are expected to have)extremely small bend radii, which are often orders of magnitude smallerthan corresponding all-polymer designs with low loss and high Q. Thesegeometric features translate into extremely high free spectral rangesfor ring modulators, compact devices, and wide process latitudes fortheir fabrication. Given the inexpensive and readily available foundrySOI and silicon processes available today, and the commercialavailability of electron beam lithography at sub-10 nm line resolution,it is expected that slot-waveguide based modulators are likely toreplace conventional modulators in many applications in the comingyears.

Waveguide Susceptibility

The primary design goal of any electro-optic waveguide geometry is tomaximize the amount of shift in effective index that can occur due to anexternal voltage. The exact modal patterns for these waveguides can becalculated using a Hermetian eigensolver on the FDTD grid. Once themodal patterns are known, the shift in effective index due to an indexshift in part of the waveguide can be readily calculated. The staticelectric field due to the two waveguide arms acting as electrodes can becalculated by simply solving the Poisson equation.

The use of nonlinear polymers with slot waveguides provides ananisotropic effect on the local dielectric constant of the material whenexposed to an electric field. The local shift in relative dielectricconstant for the optical frequency can be expressed as in Eqn. (4)above.

Consider the x-y plane to be the plane of the waveguide, while the zdirection is the direction of propagation. In this case, the total shiftin effective index for the optical mode can be calculated to be thatgiven in Eqn (7):

$\begin{matrix}{{\delta \; n} = {\frac{\int{{{E_{opt} \cdot v}}^{2}ɛ_{0}{w( {E_{dc} \cdot v} )}{A}}}{\int{2{{Re}( {{{Ex}_{opt}^{*}{Hy}_{opt}} - {{Ey}_{opt}^{*}{Hx}_{opt}}} )}{A}}}\frac{1}{k_{0}}{{\delta ɛ}( {n^{4}r_{33}} )}}} & (7)\end{matrix}$

The integral in the numerator is taken over only regions where thenonlinear polymer has been deposited, while the integral in thedenominator should be taken over all space. Note that Eqn. (7) presumesthat in the poling process, any region where the nonlinear polymer isexposed to a dc field is poled to the maximal extent; that is, themaximal r₃₃ will be demonstrated in the resulting material. In regionswhere the dc field is very small, this is unlikely to be the case, butthese regions already do not contribute to Eqn. (7) much anyway, so thisapproximation is unlikely to cause substantial error.

The particular strength of the polymer, however, is not directlyrelevant to the configuration of the waveguide geometry. It isconvenient to factor the last term out of Eqn (7), leaving what we willdefine as the effective index susceptibility as shown above in Eqn (6).

Here V has been introduced, the external voltage that corresponds toE_(dc). The units of the effective index susceptibility are m⁻¹. Thederivative of the effective index with respect to applied voltage isthen as shown above in Eqn. (5).

This relationship expresses how much the effective index of thewaveguide shifts in response to a change in index in one of itsconstituent parts. Before continuing, it is useful to note anapproximate maximum value for Eqn (5). In the case that the mode werecontained entirely inside a material of a given index, we would haven+δn=√{square root over (∈+δ∈)}. It is in this situation that the modeis maximally sensitive to a shift in the waveguide index. Thus, in themost sensitive case we would have the value of y as given by Eqn. (8):

γ=1(2n)(E _(dc) ·v)/V  (8)

Here it has been assumed that the dc field is uniform over the entirewaveguide region. This provides a useful approximate upper bound on theeffective index susceptibility that we can expect to obtain from anywaveguide design.

Before proceeding, however, we must consider how the performance ofvarious active devices depend on the effective index susceptibility. AMach-Zehnder modulator can be formed by having both arms made of a slotwaveguide with infiltrated nonlinear polymer. Note that in Eqn. (6),there is no constraint on the sign of the shift in index. Therefore, achange in the sign of the voltage will change the sense of the shift inindex shift. Modulator performance is often characterized by V_(π), theamount of voltage needed to obtain a relative π of phase shift betweenthe two arms. The optimal modulator design, with one arm positivelybiased and one arm negatively biased, has a V_(π) given by Eqn. (9):

$\begin{matrix}{V_{\pi} = \frac{\pi}{2k_{0}{L( {{\partial n}/{\partial V}} )}}} & (9)\end{matrix}$

Multiplying both sides by L, we have:

$\begin{matrix}{{V_{\pi}L} = \frac{\pi}{2{k_{0}( {{\partial n}/{\partial V}} )}}} & ( {9a} )\end{matrix}$

Here L is the length of the Mach-Zehnder, and k₀ is the free spacewavenumber of the optical signal under modulation. State of the artresults for Vπ's for optical modulators are currently on the order of1-5 V. The tunability of a resonator and the value 1/(V_(π)−L) for aMach-Zehnder modulator are both proportional to the figure of merit, y.Thus, increasing the figure of merit will lead to better deviceperformance for both ring and MZI geometries.

Ring resonators have also been used to enable optical signals to bemodulated or switched based on a nonlinear polymer being modulated by anexternal voltage. In this case, the performance of the tunable ringresonator is usually reported in the frequency shift of a resonance peakdue to an externally applied voltage. This can be expressed as shown inEqn. (10):

$\begin{matrix}{\frac{\partial f}{\partial V} = \frac{{- \frac{c}{\lambda}}\frac{\partial n}{\partial V}}{( {n - {\lambda \frac{\partial n}{\partial\lambda}}} )}} & (10)\end{matrix}$

Results of 1 GHz/V have recently been reported for ring resonators basedon large electrodes. We have observed 5.2 GHz/V of tuning.

Waveguide Geometries

We now describe several different waveguide geometries, and show theeffective index susceptibility as a function of the slot sizes of thewaveguide. In all cases, the modes have been solved using theaforementioned Hermetian eigensolver, and Eqn. (5). The susceptibilitiesare calculated near a 1550 nm free space wavelength. However, the valuesobtained will not vary much from 1480 nm to 1600 nm as the modal patterndoes not change significantly. In the embodiments described, thewaveguides are composed of silicon, and assumed to rest on a layer ofsilicon dioxide. The top cladding is a nonlinear polymer with an indexof 1.7. This is similar to the waveguide geometry that we have used inour modulation work described hereinabove. FIG. 32 shows the staticelectric fields solved as part of analyzing waveguide design 1 with agap of 40 nm, as described in Table 2. As one would expect, the field isnearly entirely concentrated inside the slot area. The field shown wascalculated assuming a voltage difference of 1 Volt. It is slightlylarger than simply the reciprocal of the gap size due to the singularnature of the solution to Poisson's equation near the corners of thewaveguide.

FIGS. 32A and 32B illustrate solved field patterns for the analysis ofwaveguide 1 at a 40 nm gap. FIG. 32A shows the static voltage potentialfield distribution due to charging the two electrodes. FIG. 32B showsthe electric field due to the potential distribution. |E| is plotted inincrements of 10%.

We have constrained ourselves to use waveguide geometries that haveminimum feature sizes of at least 20 nm. These are near the minimumfeature sizes that can be reliably fabricated using e-beam lithography.Table 2 lists a description of each type of waveguide studied. Eachwaveguide was studied for a number of different gap sizes. In all cases,the maximum susceptibility was obtained at the minimum gap size. Themaximum gap size studied and the susceptibility at this point are alsolisted. In some cases, the study was terminated because at larger gapsizes, the mode is not supported; this is noted in Table 2. Formultislot waveguide designs where there are N arms, there are N−1 gaps;the design presumes that alternating arms will be biased either at theinput potential or ground.

Table 2 shows the effective index susceptibility for various waveguidedesigns.

The dependence of susceptibility on gap size is presented in FIG. 33 forseveral waveguides. The susceptibility is approximately inverselyproportional to gap size.

It is clear that within the regime of slotted waveguides, it is alwaysadvantageous to make the slot size smaller, at least down to the 20 nmgap we have studied. This causes the DC electric field to increase,while the optical mode tends to migrate into the slot region, preventingany falloff due to the optical mode failing to overlap the modulationregion.

TABLE 2 Waveguide Waveguide Height Arm Sizes Maximum γ Minimum γ Design(nm) (nm) (μm⁻¹) (μm⁻¹) 1 100 300, 300 1.3, 20 nm gap .40, 140 nm gap 2150 300, 300 1.6, 20 nm gap .68, 120 nm gap 3 200 300, 300 2.3, 20 nmgap .74, 120 nm gap 4 100 400, 400 1.1, 20 nm gap .67, 60 nm gap, modallimit 5 100 250, 250 1.2, 20 nm gap .56, 60 nm gap, modal limit 6 100300, 40, 300 1.6, 20 nm gap .53, 80 nm gap, modal limit 7 100 300, 40,40, 300 1.9, 20 nm gap .76, 60 nm gap, modal limit 8 200 200, 40, 200 3,20 nm gap 1.4, 60 nm gap, modal limit 9 300 300, 300 2.5, 20 nm gap 2.5,20 nm gap, modal limit Steier et al. N/A N/A .026, 10 μm gap N/A

In examining the results of our calculations, it is useful to calculatethe maximum susceptibilities that can be obtained. For an effectiveindex of about 2, which is approximately correct for these waveguides,and a gap size of 20 nm, the maximum achievable y is approximately 12.5μm⁻¹. Thus, for a gap size of 20 nm, waveguide design 8 is alreadywithin 25% of the theoretical maximum value.

It is also worth noting the corresponding y value that can be obtainedby calculation using our methods for the separated electrode approach ofSteier. The effective index of the mode is expected to be about 1.8, andthe gap distance for the dc field is 10 um. Under the most optimisticassumptions about mode overlap with the active polymer region (that is,assuming complete overlap), this corresponds to a y of about 0.03 μm⁻¹.

It is useful to calculate, given the current r₃₃ values that areavailable, the index tuning that might be achieved with these designs.The most advanced polymers now yield r₃₃ values of 500 pm/V. If a bulkrefractive index of 1.7 is used, then a ∂n/∂V of 0.006 V⁻¹ is obtainedwith the best design given above. Using a waveguide with an effectiveindex of 2 and a group index of 3, which are typical of silicon-polymernano-slot waveguides, the V_(π) for a Mach-Zehnder with a length of 1 cmis expected to be about 6 mV. The resonance shift that is expected to beobtained in a ring resonator configuration would be 380 GHz per volt.Both of these values represent orders of magnitude improvement in theperformance of these devices compared to current designs.

Segmented Contacting

As we have shown empirically, silicon can be doped to about 0.025 Ω-cmof resistivity with a n-type dopant without substantially increasinglosses. Other dopants or perhaps other high index waveguiding materialsmay have even higher conductivities that can be induced, withoutsignificantly degrading optical performance. However, it is known thatthe conductivity cannot be increased endlessly without impacting opticalloss.

This naturally presents a serious challenge for the issue of driving aslot waveguide of any substantial length. Consider a slot waveguide armof length 1 mm, formed of our optimal design. The capacitor formed bythe gap between the two electrodes is about 0.25 pF. The ‘down the arm’resistance of the structure, however, is 4 MΩ. Therefore, the turn ontime of an active waveguide based on this is about 0.1 μS, implying a 10MHz bandwidth.

A solution to this problem is presented by continuously contacting thewaveguide via a segmented waveguide. This comprises contacting the twosilicon ridges with a series of silicon arms. Even though the siliconarms destroy the continuous symmetry of the waveguide, for the properchoice of periodicity no loss occurs, and the mode is minimallydistorted. This is because a Bloch mode is formed on the discretelattice periodicity, with no added theoretical loss. Of course theperformance of fabricated devices will be different from that ofconventional slot waveguides due to fabrication process differences. Wehave previously demonstrated empirically that continuous electricalcontact can be formed for non-slotted waveguide via segmentation withrelatively low optical losses.

Here we present a simulation of a particular segmentation geometry forour optimal slot waveguide design, that with 200 nm tall and 300 nm widearms and a gap of 20 nm. We have found that a segmentation with 40 nmarms, and a periodicity of 100 nm, appears to induce no loss orsignificant mode distortion in the waveguide. Around 2 um of clearanceappears to be needed from the edge of the segmented waveguide to the endof the arms. FIGS. 34A, 34B and 34C show plots of several cross sectionsof the segmented slot waveguide with a plot of the modal patternoverlaid. For comparison, a cross section of the unsegmented slotwaveguide is presented as well. Simulations were also performed toconfirm that the index shift formula continued to apply to the segmentedslotted waveguide. It was found that the index shift was in approximateagreement with the value predicted for the non-segmented case.Non-segmented modesolvers were used for the rest of the simulations inthis work, because simulation of the segmented designs is radically morecomputationally burdensome than solving for the unsegmented case, asthey require solving for the modes of a 3d structure. Since the indexshifts for the unsegmented and segmented cases are extremely similar,solving for the modes in the unsegmented cases is adequate for purposesof design and proof-of-concept.

FIG. 34 A shows a cross section of the segmented, slotted waveguide,with the |E| field plotted in increments of 10% of max value. FIG. 34Bshows a similar plot for the unsegmented waveguide. FIG. 34C shows ahorizontal cross section of the segmented, slotted waveguide; Re(Ex) isplotted in increments of 20% of max. In an actual device, some sort ofmetal based transmission line would undoubtedly provide the drivingvoltage for the waveguide. The metal electrodes that would likely formpart of this transmission line have been noted in FIG. 34C. In all casesthe mode has been normalized to have 1 Watt of propagating power. FIG.34A and FIG. 34C show the location of the other respective cross sectionas a line denoted C in FIG. 34A and A in FIG. 34C.

Assuming a 0.025 Ω-cm resistivity, one can calculate the outer armresistance as 63 kΩ per side per period, while the inner arm resistanceis 25kΩ per side per period. The gap capacitance per period is 2.5×10⁻¹⁷Farads. This implies a bandwidth on the order of 200 GHz.

We now describe an electro-optic modulator fabricated from a siliconslot waveguide and clad in a nonlinear polymer. In this geometry, theelectrodes form parts of the waveguide, and the modulator drivingvoltage drops across a 120 nm slot. As a result, a half wave voltage of0.25 V is achieved near 1550 nm. This is one of the lowest values forany modulator obtained to date. As the nonlinear polymers are extremelyresistive, our device also has the advantage of drawing almost nocurrent. It is believed that this type of modulator could operate atexceedingly low power.

A unique advantage with nonlinear polymers is that an integrated opticalcircuit can be conformally coated by a nonlinear polymer. This property,when combined with a slot waveguide, enables the construction of auniquely responsive modulator. We describe the use of a push-pullMach-Zehnder modulator configuration in which each arm has an opposingbias, leading to an opposing phase shift.

FIG. 35( a) shows the slot waveguide used for the Mach-Zehndermodulator. The modal pattern near 1550 nm is plotted, and contours of|E| are shown. FIG. 35( b) is an SEM micrograph of a slot waveguide. Inthis case, the slot waveguide is being coupled to with a ridgewaveguide; this mode converter involves tiny gaps which ensureelectrical isolation between the two arms. Contacting arms are alsopresent around 3 μm from the ridge/slot junction. The dimensions are two300×100 nm arms separated by a 120 nm slot.

Nonlinear polymers typically have very high resistivity of 10¹¹ Ωcm. Asa result, the two silicon arms are electrically isolated and can be usedas modulator electrodes. The voltage drop between the arms occurs acrossa 120 nm electrode spacing, as opposed to the 5-10 μm that is typicallyrequired for modulators involving a nonlinear polymer and metalliccontacts. This is a fundamental advantage that slot waveguide geometrieshave for electro-optic modulation.

It is advantageous to contact the silicon arms with an externalelectrode throughout the length of the Mach-Zehnder device to minimizeparasitic resistances. We use a segmented waveguide in which a periodicset of small arms touches both waveguide arms. We use a segmentationwith a periodicity of 0.3 μm and arm size of 0.1 μm that is largelytransparent to the optical mode.

Because the polymer has a second order nonlinearity, a Mach-Zehndermodulator can be operated in push-pull mode, even with no dc bias,effectively doubling the modulator response. FIG. 36( a) is a diagram ofthe modulator layout. Contacts A, B, and C are shown. FIG. 36( b) andFIG. 36( c) are two SEM micrographs that show the slotted, segmentedregion, as well as the location where the silicon makes contact with theelectrical layer.

Devices were fabricated with electron beam lithography and dry etching.The second order nonlinear polymer YLD 124 doped 25% by weight into aninert host polymer (APC), was used as a coating. Mixing and poling weredone in the standard fashion, and a poling field of 150 V/μm was used.Coupling on and off the chip was accomplished via grating couplers,which had a bandwidth of around 40 nm. Total device insertion losseswere approximately −40 dB fiber to fiber.

Referring to FIG. 36( a), there are three regions in the modulator thatare capable of maintaining distinct voltages. During poling operation,contact A is given a voltage of 2V_(pole), contact B a voltage ofV_(pole), and contact C is held at ground. To achieve a poling field of150 V/μm, V_(pole) was 18 V. This has the effect of symmetricallyorienting the polymer in the two Mach-Zehnder arms. During deviceoperation, contact B is driven at the desired voltage, while contacts Aand C are both held at ground, leading to asymmetric electric fields inthe two arms for a single bias voltage. This is the source of theasymmetric phase response. Electrical regions A and C cross thewaveguide by means of a slotted ridged waveguide. At the ridge to slotmode converter, a small gap is left that maintains electrical isolationbut is optically transparent. This enables the device to be builtwithout requiring any via layers. A driving voltage from a DC voltagesource was applied to contact B, while contacts A and C were held atground.

We believe that there is the possibility of constructing even narrowerslot waveguides, on the scale of 1-5 nm in thickness. For example, onecould use epitaxial techniques to grow a horizontal slot structure(rather than the vertical structures we have explored thus far) with anactive, insulating material, with silicon beneath and above. This couldbe done in a layer form analogous to SOI wafer technology, in which avery thin layer of electroactive material such as the polymers we havedescribed herein could be introduced. Such structures offer thepossibility of yet another order of magnitude of improvement in thelow-voltage performance of modulators. Here we should also mention thatwe anticipate our slot structures to be fairly robust even in thepresence of fabrication errors. Fabrication imperfections may cause someof the narrower slots to have tiny amounts of residual silicon or oxidein their centers, or to even be partially fused in places. As long aselectrical isolation is obtained, and the optical loss is acceptable, wewould expect the slot performance to decrease only in a linearproportion to the amount of the slot volume that is no longer availableto the nonlinear polymer cladding.

Table 4 presents some estimated performance parameters for a number ofstrip loaded lumped element waveguides. In all instances, a value ofV_(π) of 0.25 volts is used as a design parameter.

TABLE 4 Device Internal Drive Polymer Power Power Length Gap C_(gap)Activity Vπ Consumption @ @ 50 Ω f_(3 dB) (mm) (nm) (fF) (pm/V) (V) 20GHz (μW) (μW) (GHz) Optimizing 1.65 30 500 73 0.25 312 625 22 Polymer0.4 30 120 300 0.25 75 625 90 Length 2.75 50 500 60 0.25 312 625 22Polymer 0.55 50 100 300 0.25 63 625 110 Length 5.5 100 500 68 0.25 312625 22 Polymer 1.2 100 108 300 0.25 68 625 100 Length

Optimizing to reduce length also serves to reduce losses. For lengthsgreater than about 2 mm, the lumped element analysis is expected tobreak down. As previously indicated, there exist polymers with activityof approximately 600 pm/volt. It is expected that surface treatment willimprove the optical losses as discussed hereinabove.

While the present description has been presented with regard toelectro-optic materials that require poling, the inventors alsocontemplate the use of use of self-assembled EO materials in the slot toeliminate the need for poling.

We now present illustrative embodiments for devices that employwaveguides that enhance the nonlinearity that an optical mode wouldexperience from a nonlinear polymer cladding, such as the slotwaveguides in silicon-on-insulator substrates which concentrate thefield sharply in the center of a slot, such as shown in FIG. 4.Third-order nonlinear polymers such as those described hereinabove, forexample with regard to FIG. 22 and FIG. 26, can be deposited over thechip and in particular in this slot, thus enabling the field enhancementto greatly increase the effective nonlinearity of a nano-scale SOIwaveguide clad with nonlinear polymer as compared to, for example, asimple ridge waveguide design. In some embodiments, polymers exhibitinghigher odd order nonlinear optical coefficients can also be used as theoptically responsive medium.

Several illustrative designs are provided for devices that are believedto be practical with the higher available nonlinearities, and whichcould be integrated on chip in a silicon-polymer system. Using a seriesof Mach-Zehnder all-optical switches based on the Kerr effect, whichbecome practical with higher nonlinearities, one can construct avariable delay line of particularly high switching speed. These devicesare expected to be capable of multiplexing bitstreams into speed regimesthat have heretofore been inaccessible. An illustrative design for aself-oscillator device is provided, which can employ several CW opticalsignals and generate a pulsed signal, by virtue of having the output ofa Mach-Zehnder all-optical switch turn the switch on or off, dependingon the state of the switch. An illustrative design for a clock signalgenerator operating at extremely high frequencies is provided in which asquare wave clock signal at a first frequency is used as input, and thefrequency is increased by use of an AND gate and a series of delaylines, to produce a clock multiplier.

Each of the designs includes at least one input port that accepts anoptical input signal, an output port at which an output optical signalappears or is provided, and an interaction region having at least oneoptical input signal that defines an interaction between the at leastone input signal and another optical signal (including possibly a copyor a portion of the input signal itself). In general, the interactionregion includes an input port (for example, a gate input port, a clockinput port, a pump input port or the like) if there is only one inputport for an input signal, but may not have an input port if there are aplurality of input ports for input signals (such as in an AND gate,which has two input ports, and in which the interaction region islacking a gate input port).

One of the most significant problems in integrated optics is how toachieve low power, high speed all optical modulation and switching.There are many applications that would emerge if this problem could besolved. In particular, it would become possible to build high speedall-optical clocks and logic circuits that can operate at speeds farexceeding that of conventional electronics. We describe an expectedsolution of this problem through the use of patterned opticallyabsorbing materials, which can be organic, inorganic, or a combinationor hybrid of the two.

Optically Absorbing Materials

It is possible to synthesize and deposit polymers and other materialsthat absorb light at one wavelength, for instance 600 nm, and that aretransparent at other nearby wavelengths, such as 700 nm. This is oftendue to a resonance in the absorbing material, where an electron makes atransition from one state to another. It is further possible to designmaterials that, once this transition occurs, also change their opticalproperties at non-resonant wavelengths. It is possible, for instance,for these materials to have their refractive indices shiftsignificantly, due to the absorption of a photon. It is also possiblefor their optical losses at other wavelengths to change dramatically.Examples that are well known include PhotoGrey eyeglass lenses availablefrom Corning Glass and Transitions™ eyeglass lenses available fromTransitions Optical, Inc., 9251 Belcher Road Pinellas Park Fla. 33782.These lenses darken when exposed to UV radiation. The lens materialabsorbs the UV but passes light in the visible portion of the spectrum,with a reduction in the intensity of the visible light. The Photgreymaterial relies on inorganic microcrystalline material dispersedthroughout the lens, while the Transitions™ material is an organic thinfilm that is localized in a region of the lens, such as a surface of thelens.

In some instances, the response of organic materials can be very fast.In some instances; as soon as a photon is absorbed at resonance, thestate of the molecule can change in times of 100 fs or less. Further,the absorbing materials can be designed so that they will relax backinto their initial state in time periods of 1 ps or less. Takentogether, this means that these materials are capable of opticalswitching at very high speeds, often in excess of 1 THz.

Polymeric materialscan be synthesized and designed ab-initio, so theresonances that they exhibit can be tuned. The design of all opticallogic gates can take advantage of specifically designed properties thatmay be present in such organic materials. Other materials can also beconstructed with tunable absorptions.

As has been described hereinabove, it is possible to construct low loss,high index contrast waveguides by etching a semiconductor or glassmaterial, and by applying either electron beam lithographic orphotolithographic methods. The waveguides can guide optical radiation,with optical modes that are often far sub micro-meter ( 1/1,000,000 of ameter) in lateral size. Silicon is an excellent example of thisbehavior. Low loss waveguides can be prepared to handle radiation from1200 nm to 2000 nm in free space wavelength. At lower free spacewavelengths, other materials can be used in a similar fashion.

FIG. 37 is an SEM micrograph a silicon ridge waveguide about 0.5 μm widethat is used in a y-junction coupler.

Using slot waveguides, it is further possible to make the effective modesize exceptionally small. We have shown that it is possible to getradiation with a free space wavelength of 1550 nm to propagate in aneffective region only 40 nm×200 nm. See FIG. 35( a) and FIG. 35( b).

Design of an all-Optical Switch

An all optical switch can be built on the basis of the absorptivepolymer or other material and a Mach-Zehnder interferometer. FIG. 38shows the basic layout. One arm of the Mach-Zehnder involves inducing agate optical mode. Consider the situation in which the gate mode is atthe resonance frequency of the absorbing material, while the signal modeis off of resonance. In this circumstance, the signal mode willpropagate with minimal loss through the structure, but the gate modewill be readily absorbed by the absorbing material, shifting the indexdramatically. This index shift causes the signal mode to experience aphase shift in one arm. If the phase shift reaches a value of an oddmultiple of a radians, the Mach-Zehnder will turn off (e.g., an outputintensity will be substantially zero). FIG. 38 is a schematic diagramshowing an illustrative design of an all-optical switch.

Another design for an all optical switch involves the use of an inducedphoto-absorption in the absorbing material. In such a case, aMach-Zehnder interferometer is not needed, because the switching can bemade to occur based on a direct intensity modulation. In this design,the gate mode will be guided so that it propagates in the same waveguideas the signal mode.

Design of Chained or Cascaded all-Optical Logic

A single gate such as that shown in FIG. 38 is of limited utility. Theutility of the approach we describe here is due to the fact thatmultiple gates can be constructed on a single substrate. As mentionedbefore, optically absorptive materials can be synthesized to absorb atmultiple wavelengths. It is not required that the optically absorptivematerials be patterned with a high resolution. One can simply depositthe absorbing material on the region of the switch. One can, as a resultof this, chain multiple gates together. FIG. 39 illustrates thisprocess.

FIG. 39 is a schematic diagram showing an illustrative design of multistage logic gate with two types of absorbing materials. The deviceillustrated in FIG. 39 can be fabricated by first defining waveguideswith high resolution lithography. Then, an absorbing material can bedeposited on each switch with processing steps that do not require highresolution lithography or patterning.

The two gates work together as is now described. Gate 1 operates at theresonance of absorber material 1. It switches signal 1, which is thenused as the gate signal for the secons switch on the right. Outputsignal 1 is designed to operate at the resonance frequency of material2. Output signal 1 operates as the gate signal that switches signal 2.Signal 2 can be at the same wavelength as gate 1, and can then be usedas a gate signal for further gates utilizing absorber 1. As a result, aself-controlling logic system can be created. Such systems may findapplication as all optical memory, optical processors, and generalizedlogic elements. The system can be extended to more than two wavelengthsby including regions where there are materials with absorption peaks atother wavelengths.

Resonant Enhancement

It is possible to enhance the all-optical switching effect through theuse of a resonance in the waveguide geometry. In one embodiment, theoptical path of the signal is folded back so that it utilizes the sameregion of refractive index shift multiple times. This effectivelyincreases the amount of switching that can be obtained from a givenamount of gate power.

One geometry that is possible is a resonator which has a resonance nearthe signal wavelength. As shown in FIG. 40, a ring resonator can beused. No reference arm is needed, as in the Mach-Zehnder switch, and sothis type of switch might have a smaller overall size. FIG. 40 is aschematic diagram showing an illustrative design of an all opticalswitch comprising a ring resonator. Another geometry that might servethe same purpose would be a Fabry-Perot type cell or a distributedfeedback (DFB) type geometry. Both the gate and signal optical modestravel around the ring resonator, which can be formed of a circularregion (or other closed loop) of waveguide. The gate optical mode isquickly absorbed, however.

Another possibility is to make a waveguide with a periodic structurewith a band edge near the signal frequency. Examples include aFabry-Perot type cell or a distributed feedback (DFB) type geometry thatcan serve the same purpose. The periodic structure could be designed tonot affect the gate optical frequency. A slight shift in index couldresult in the band edge moving, and the signal mode being allowed topropagate. This could also greatly increase the effective switching thatcan be obtained from the optical material. FIG. 41 is a schematicdiagram showing an alternative design for resonant enhancement using anabsorption based index shift.

Applications

Contemplated applications include: the use of nano-scale ridge, rib orslot waveguides combined with a nonlinear polymer cladding to enhancethe nonlinearity of a waveguide; the use of nonlinear polymer-clad slotand ridge nano-scale waveguides to construct a variable delay line withall-optical switches; the use of nonlinear polymer-clad slot and ridgenano-scale waveguides to construct a multiplexer or demultiplexer basedon a high speed all-optical switch; the use of nonlinear polymer-cladslot and ridge nano-scale waveguides to construct a self-oscillator byfeeding the output of an all-optical switch through an amplification andconversion waveguide and then used as the gate optical mode of theself-oscillator; the use of nonlinear polymer-clad slot and ridgenano-scale waveguides to construct a logic gate, such as an AND gate, anOR gate, a NAND a NOR, and an XOR gate; and the use of nonlinearpolymer-clad slot and ridge nano-scale waveguides to construct anultrafast clock multiplier based on a combination of an all-optical ANDgate and a series of delay lines used to recombine the pulses that canbe created in this fashion.

Theoretical Discussion Optical Rectification Theory

The general governing equation of nonlinear optics is known to be:

D _(i)=∈₀(∈_(r) E _(i)+χ_(ijk) ² E _(j) E _(k)+ . . . )  (11)

Our EO polymers are designed to exhibit a relatively strong χ² moment,ranging from 10-100 pm/V. In most χ² EO polymer systems, the Pockel'seffect is used to allow the electric field (due to a DC or RF modulationsignal) to modify the index of refraction. In such systems themodulating electric field is typically far in excess of the electricfield from the optical signal and the term that produces the materialbirefringence is the only term of importance in the above equation.

Our waveguides, however, have a very large electric field as most of theradiation is confined to a 0.01 square micron cross section. It can beshown that the electric field is approximately uniform in the transversedirection, with a magnitude of

$\begin{matrix}{10^{8}\sqrt{P}\frac{V}{m}} & (12)\end{matrix}$

where P is the optical power in Watts. At large optical fields, thenon-Pockels terms involved in the governing nonlinear equation cannot beneglected. For coherent input power, at a given location in thewaveguide, the optical field is:

E _(optical)(t)=A cos(wt+θ)  (13)

The term

$\begin{matrix}{E_{optical}^{2} = {{\frac{A^{2}}{2}{\cos ( {2( {{wt} + \theta} )} )}} + \frac{A^{2}}{2}}} & (14)\end{matrix}$

will therefore contain not only frequency doubled components, but also a“DC” component. This phenomenon is known as optical rectification. Webelieve that this DC component provides a likely explanation for thephoto-current that we observe. Because we have positioned electrodes(the two sides of the slot waveguide) at precisely the bounds of theinduced field, the effect of optical rectification takes a small sliceof the optical power and converts it into a virtual voltage sourcebetween the two arms. This in turn induces a current that we can measureand is linearly proportional to the input power E_(optical) ².

Now let us consider the solution to Maxwell's equation in more detail.Our system can be approximated for this discussion as having twodimensions, with both the optical and DC electric field in the xdirection and propagation in the z direction, for instance. Let usimagine that the χ² is nonzero and small for a tiny region from 0 to win the x dimension. χ² is sufficiently small that the electric field dueto the optical mode is still uniform. Let us imagine the system has nocharge anywhere. The optical electric field can be written asE=Ae^((ikz-iwt))+c.c. where c.c. indicates a complex conjugate. Let usfurther assume that the rectified DC field is of real amplitude C anduniformly directed in the x dimension on (0, w), and 0 elsewhere.

Other than the divergence condition, Maxwell's equations are stillsatisfied by this system. But at the edge of an interface on theinterior, the DC frequency component of D_(x), the displacement electricfield, is discontinuous. At x0, we have:

D_(x) ⁻=0  (15)

D _(x) ⁺=∈₀(∈_(r) C+χ ² C ²+2χ² |A| ²)  (16)

We neglect χ²C² because we expect the amplitude of the rectified fieldto be far smaller than that of the optical field. Clearly, the boundarycondition of zero divergence can only be satisfied if D_(x) ⁺ is 0.Then,

$\begin{matrix}{C = {{- \frac{2\chi^{2}}{ɛ_{r}}}{A}^{2}}} & (17)\end{matrix}$

Thus the direction of the rectified field is reversed compared to thedirection of χ². Note that there is no particular direction associatedwith the optical field as it is continually oscillating. As we haveseen, this rectified DC field would then, if acting as a virtual voltagesource, create an effective positive terminal on the positive pollingterminal.

Analysis of Data for Optical Rectification

To derive the magnitude of the expected photocurrent, we assume that theχ² magnitude relating to the Pockels' effect is similar to that foroptical rectification. A measurement of χ² can then be obtained from thedirect observation of the electro-optic coefficient by the standardmeasurements described earlier. The typical measured tuning value of 2GHz/V yields approximately 50 pm/V.

In the best case, devices with 6 dBm of input power returnedapproximately 1.4 nA of current. With Qs ranging from 3k to 5k, andassuming approximately 7 dB of insertion loss in the input gratingcoupler on one of our chips, in the best case as much as 0 dBm might becirculating in a resonator on resonance. This implies a peak electricfield due to the optical signal of approximately 3.1×10⁶ V/m. Theinduced static nonlinear polarization field is then nearly 1000 V/m,which amounts to a voltage drop of 14×10⁻⁵ V across a 140 nm gap. Ifthis voltage is assumed to be perfectly maintained, and the loadresistance is assumed to be 5 MΩ, then 28 pA would be generated, about afactor of 100 less than is observed in the largest measurement made, butwithin a factor of 20 of the typical measurement of 352 pA for 6 dBm ofinput. Significantly, because the generated current is quadratic in E,it is clear that the current will be linearly proportional to the inputintensity. This is in accordance with our observations. The best resultsfor optical rectification were obtained with YLD 124/APC polymer,whereas our best Pockels' Effect results were obtained with thedendrimer materials. It is believed that acceptable performance can beattained for peak electric fields of the order of 1×10⁵ V/m (that is inthe range of 1×10⁵ V/m to 9×10⁵ V/m) that are generated due to opticalsignals. It is further believed that acceptable performance can beattained for peak electric fields of the order of 1×10⁴ V/m (that is inthe range of 1×10⁴ V/m to 9×10⁴ V/m) that are generated due to opticalsignals.

Significantly, the sign of the output current matches that which wouldbe predicted by nonlinear optical rectification, as discussed above.Specifically, since positive current emanates from the positiveterminal, the rectified E field has a sign reversed from the % and thepolling E field. It is well established that the χ² direction tends toalign with the direction of the polling E field. Because of this, therectified field acting as a voltage source will produce an effectivepositive terminal at the terminal that had the positive polling voltage.

We do not yet fully understand the current generation mechanism. Inparticular, it is not clear what provides the mechanism for chargetransport across the gap. The APC material in which the nonlinearpolymer is hosted is insulating, and though it does exhibit thephotoconductivity effect due to visible light, it is unclear whether itcan for near-infrared radiation. Photoconductivity due to secondharmonic generation may play a role in this effect. It is certainly thecase, however, that current flows through this gap; that is the onlyregion in the entire system where an electromotive force exists. Also,photoconductivity alone is not adequate to explain the reversal of thecurrent coming from the detector devices when the poling direction isreversed, nor the conversion of the optical input into directed currentin general. The only mechanism to our knowledge that adequately explainsthis data is optical rectification.

If we assume that it will be possible to achieve a 10-fold improvementin the Q's of the resonators, while still getting more than 10 dB ofextinction, then the intensity circulating in such a ring would be about13 dB up from the intensity of the input wave. By comparison, with a Qof about 1000 and high extinction, the peak circulating intensity isabout the same as the intensity in the input waveguide. Therefore, it isreasonable to expect that it will be possible to get at least 10 dB ofimprovement in the circulating intensity, and thus in the conversionefficiency, by fabricating higher Q rings.

By combining the nano-scale slotted waveguide geometry withelectro-optical polymers having high nonlinear constants, we haveobtained massive enhancement of the optical field. That has in turnenabled us to exploit nonlinear optical processes that are typicallyonly available in the kW regime in the sub-mW regime. This difference isso considerable that we believe it represents a change in kind for thefunction of nonlinear optical devices. In addition, it is believed thatthis hybrid material system provides systems and methods for creatingcompact devices that exploit other nonlinear phenomena on-chip.

Optical rectification based detectors can have many advantages overcurrently available technology. In particular, such detectors areexpected to function at a higher intrinsic rate than the typicalphotodiode in use, as the optical rectification process occurs at theoptical frequency itself, on the order of 100 THz in WDM systems. Theabsence of an external bias, and the generation of a voltage rather thana change in current flow, both provide certain advantages in electronicoperation. We also believe that a device based on nonlinear opticalrectification will not suffer from the limitation of a dark current.This in turn can provide WDM systems that will function with loweroptical power, providing numerous benefits. Similarly, our demonstrationof enhanced modulation using these waveguide geometries provides usefulcomponents for future communications systems.

We conclude by stressing advantageous economic aspects of our inventionin various embodiments. Because our devices can be fabricated in planarelectronics grade silicon-on-insulator, using processes compatible withadvanced CMOS processing, it is expected that devices embodying theseprinciples will be less expensive to fabricate.

While the present invention has been particularly shown and describedwith reference to the structure and methods disclosed herein and asillustrated in the drawings, it is not confined to the details set forthand this invention is intended to cover any modifications and changes asmay come within the scope and spirit of the following claims.

1. An all-optical signal processing device, comprising: an optical inputof said all-optical signal processing device configured to accept anoptical signal as input; an optical output of said all-optical signalprocessing device configured to provide a modulated optical signal asoutput; and a plurality of interaction regions configured to permit saidoptical input signal to interact in each of said plurality ofinteraction regions with a selected cladding comprising a material thatexhibits enhanced optical absorption of one or more input signals toproduce one or more modulated optical output signals, said interactionregion comprising a high index contrast waveguide adjacent an insulatingsurface of a substrate.
 2. The all-optical signal processing device ofclaim 1, wherein each of said plurality of interaction regions isconfigured to permit said optical input signal to interact with at leastanother optical signal.
 3. The all-optical signal processing device ofclaim 1, wherein said high index contrast waveguide is a selected one ofa ridge waveguide, a rib waveguide and a slot waveguide.
 4. Theall-optical signal processing device of claim 3, wherein said high indexcontrast slot waveguide has at least two stripes defining said slot; andat least some of said cladding is situated within said slot.
 5. Theall-optical signal processing device of claim 1, wherein said substrateis a silicon wafer.
 6. The all-optical signal processing device of claim5, wherein said insulating surface is a layer comprising silicon andoxygen.
 7. The all-optical signal processing device of claim 1, whereinsaid substrate is selected from one of silicon-on-insulator (SOI) andsilicon-on-sapphire (SOS).
 8. The all-optical signal processing deviceof claim 1, wherein said slot is less than or equal to 100 nanometers inwidth.
 9. The all-optical signal processing device of claim 1, whereinsaid optical input comprises an input waveguide for coupling opticalradiation into said high index contrast waveguide.
 10. The all-opticalsignal processing device of claim 1, wherein said all-optical signalprocessing device is a logic gate.
 11. The all-optical signal processingdevice of claim 10, wherein said logic gate is a selected one of an ANDgate, an OR gate, a NAND a NOR, and an XOR gate.
 12. The all-opticalsignal processing device claim 1, wherein said all-optical signalprocessing device is a selected one of an optical latch and an opticalmemory.
 13. The all-optical signal processing device of claim 1, whereinsaid all-optical signal processing device is a variable delay line. 14.The all-optical signal processing device of claim 1, wherein saidall-optical signal processing device is a self-oscillator.
 15. Theall-optical signal processing device of claim 1, wherein saidall-optical signal processing device is a multiplexer.
 16. Theall-optical signal processing device of claim 1, wherein saidall-optical signal processing device is a demultiplexer.
 17. Theall-optical signal processing device of claim 1, wherein saidall-optical signal processing device is a selected one of a clock and aclock multiplier.
 18. The all-optical signal processing device of claim1, wherein said cladding material is infiltrated into a slot of a slotwaveguide.
 19. The all-optical signal processing device of claim 1,wherein said cladding material, upon absorbing single or multiplephotons of one frequency, produces a local change in refractive index ordielectric constant for propagating modes of another frequency.
 20. Theall-optical signal processing device of claim 1, wherein a systemcomprises a plurality of such devices on the same substrate, each ofwhich may comprise different cladding materials.